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In order to compress bandwidth, Cb and Cr are sampled at a lower rate than Y, which is technically known as "chroma subsampling." This means that some color ...
I.J. Information Engineering and Electronic Business, 2014, 2, 28-34 Published Online April 2014 in MECS (http://www.mecs-press.org/) DOI: 10.5815/ijieeb.2014.02.03

New Contribution on Compression Color Images: Analysis and Synthesis for Telemedicine Applications Beladgham Mohammed Bechar University/Department of Electronic, Bechar, 08000, Algeria Email: [email protected] 1

Habchi Yassine, 2Moulay Lakhdar Abdelmouneim, 3Bassou Abdesselam, 4Taleb-Ahmed Abdelmalik

Bechar University/Department of Electronic, Bechar, 08000, Algeria Email: [email protected], [email protected], [email protected],[email protected]

Abstract—The wavelets are a recent tool for signal processing analysis, for multiple time scale. It gives rise to many applications in various fields such as geophysics, astrophysics, telecommunications, imaging, and video coding. They are the basis of new analytical techniques and signal synthesis and some nice applications for general problems such as compression. This paper introduces an application for color medical image compression based on the wavelet transform coupled with SPÏHT coding algorithm. In order to enhance the compression by this algorithm, we have compared the results obtained with wavelet transform application in natural, medical and satellite color image field. For this reason, we evaluated two parameters known for their calculation speed. The first parameter is the PSNR; the second is MSSIM (structural similarity)

II. CLASSICAL WAVELET TRANSFORM In separable 2D case, classical discrete wavelet transform (DWT) can be realized with convolutional Mallat’s algorithm in Fig 1. Li nes

H

2 1

H

G

Colu mns

1 2

Aj f

1 2

D1j f

1 2

D2 2j f D jj f1

1 2

D 3j f

A j 1 f H

2 1

G Index Terms—DWT, color image, lifting scheme, SPIHT.

G

Fig 1: 2D DWT implementation

A f A j 1 f A j 1 f

I. INTRODUCTION Reduction technologies debit have long been used, but it is only recently that they have become simple enough for everyday application such as for distance diagnostic medical system, digital library and Internet…One of the most important problems in such applications is how to store and transmit images [1]. For this the researchers are interested by medical diagnostic field to help the doctor in his diagnostic work. The search for a good representation is a central problem of image processing for this, many ideas that have already been studied for search and to come determine a bases adapted to complex geometry presented in the content of images. Image representations in separable orthonormal bases such as Fourier, local Cosine can not take advantage of the geometrical of image structures. Standard wavelet bases are optimal to represent functions with piecewise singularities.

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The low-pass and high-pass decomposition filters are represented as H and G , respectively. Applying H and G both in horizontal and vertical directions to the original image I (i, j), and next, recursively to the resulting gradually coarser coefficients, we can obtain the following decomposition coefficients. Akj,l f 



  h2k  n h2l  m Anj,m1 f

(1)

n   m    

D1j ,k ,l f  D 2j ,k ,l f 

D 3j ,k ,l f 



  h2k  n g 2l  m Anj,m1 f

(2)

  g 2k  n h2l  m Anj,m1 f

(3)

  g 2k  n g 2l  m Anj,m1 f

(4)

n   m     n   m    

n   m  

I.J. Information Engineering and Electronic Business, 2014, 2, 28-34

New Contribution on Compression Color Images: Analysis and Synthesis for Telemedicine Applications

The sub-bands are labeled by using the following symbols: 1. LLn ( Akj,l f ) is the approximation image at resolution (level decomposition) n, indicate low-frequency component (LL) resulting from low-pass filtering in the vertical and horizontal directions. 2. HLn ( D 1j , k ,l f ) represents the vertical details at resolution n, and results from vertical low-pass filtering and horizontal high-pass filtering. 3. LHn ( D 2j , k ,l f ) represents the horizontal details at resolution n, and results from horizontal low-pass filtering and vertical high-pass filtering. 4. HHn D 3j , k ,l f represents the diagonal details at resolution n, and results from high-pass filtering in both directions.

X X 0 n  X 2n  1 that denote all even-indexed and odd-indexed samples of X , respectively [7]. 2. Lifting: In this module, the prediction operation P is used to estimate X 0 n from X e n and results in an

error signal d n which represents the detailed part of the original signal. Then we update d n by applying it to the update operation U , and the resulting signal is combined with X e n to sn estimate, which represents the smooth part of the original signal. 3. Scaling: A normalization factor is applied to d n and sn , respectively. In the even-indexed part sn is multiplied by a normalization factor K e to produce the wavelet subband X L1 . Similarly in the odd-index part the error signal d n is multiplied by K 0 to obtain the wavelet subband X H 1

X e n X n 

Split

Splitting

I (i, j) can be equivalently represented as the more compact form below.



I i, j   A j , D1j , D 2j , D 3j ,..., A 1 , D H1 , DV1 , D D1



(5)

III. LIFTING SCHEME The wavelet transform (WT), in general, produces floating point coefficients. Although these coefficients are used to reconstruct an original image perfectly in theory, the use of finite precision arithmetic and quantization results in a lossy scheme. Recently, reversible integers WT’s (WT's that transform integers to integers and allow perfect reconstruction of the original signal) have been introduced [2,3]. In [4], Calderbank et al. introduced how to use the lifting scheme presented in [5], where Sweldens showed that the convolution based biorthogonal WT can be implemented in a lifting-based scheme as shown in Fig. 1 for reducing the computational complexity. The lifting-based WT consists of splitting, lifting, and scaling modules and the WT is treated as a prediction-error decomposition. It provides a complete spatial interpretation of WT. In Fig. 3, let X denote the input signal, and X L1 and X H 1 be the decomposed output signals, where they are obtained through the following three modules of lifting-based 1DWT: 1. Splitting: In this module, the original signal X is divided into two disjoint parts, X e n  X 2n and Copyright © 2014 MECS

+ -P

X 0 n

Fig 2: Wavelet Filter Decomposition

29

Ke

X LI

K0

X HI

U

+ Lifting

Scaling

Fig 3: The lifting-based WT [7]

Note that the output results of X L1 and X H 1 obtained by using the lifting based WT are the same as those of using the convolution approach for the same input even if they have completely different functional structures. Compared with the traditional convolution-based WT, the lifting-based scheme has several advantages. First, it makes optimal use of similarities between the highpass and lowpass filters; the computation complexity can be reduced by a factor of two. Second, it allows a full in place calculation of the wavelet transform. In other words, no auxiliary memory is needed.

IV. EZW CODING SCHEME The algorithm proposed by Shapiro [18], the design of this algorithm is based on two pass with a calculated threshold T, we determine the maximum value of the wavelet coefficients, so in the first dominant pass, if the coefficient absolute value is greater than the threshold, so we obtained a positive code or negative code according to the sign of coefficient, if the absolute value is less, we check the descendants coefficient, if you have a coefficient with absolute value above the threshold, we obtained IZ code, else we have a code ZT. In the second pass, the comparison is made in the middle of the interval [Tn, 2Tn[, if this coefficient belongs to the first interval, so we are a transmission of

I.J. Information Engineering and Electronic Business, 2014, 2, 28-34

30

New Contribution on Compression Color Images: Analysis and Synthesis for Telemedicine Applications

the bit 1, if this coefficient belongs to the second interval, so there are a transmission of bit 0.

V. SPIHT CODING SCHEME The SPIHT algorithm proposed by Said and Pearlman in 1996 [19], ameliorate progressive algorithm is compared to the EZW algorithm, based on the creation of three list SCL, ICL and ISL with a calculated threshold T, each time you make a scan on both lists SCL and ISL and that for the classified the significant coefficient in the list of significant coefficient.

VI. QUALITY EVALUATION PARAMETER The Peak Signal to Noise Ratio (PSNR) is the most commonly used as a measure of quality of reconstruction in image compression. The PSNR were identified using the following formulate:

MSE 

 1 M 1 N 1   .   I  i, j  I  i, j  M.N i 0 j0  

2

(6)

Mean Square Error (MSE) which requires two MxN gray scale images I and Iˆ where one of the images is considered as a compression of the other is defined as:

compressed by wavelet transform, based on the assumption that the human visual system (HVS) is highly adapted to extract structural information. The similarity compares the brightness, contrast and structure between each pair of vectors, where the structural similarity index (SSIM) between two signals x and y is given by the following expression:

SSIM  x, y   l  x, y  c  x, y  s  x, y  (9) Finally the quality measurement can provide a spatial map of the local image quality, which provides more information on the image quality degradation, which is useful in medical imaging applications. For application, we require a single overall measurement of the whole image quality that is given by the following formula:

 

MSSIM I, ˆI 



1 M  SSIM Ii , ˆIi M i 1



(10)

Iˆ are respectively the reference and degraded images, I i and Iˆi are the contents of images at Where I and

the i-th local window. M: the total number of local windows in image. The MSSIM values exhibit greater consistency with the visual quality.

• The PSNR is defined as: VII. ALGORITHM

PSNR  10.log10

2

R

 1

MSE

2

dB

(7)

Usually an image is encoded on 8 bits. It is represented by 256 gray levels, which vary between 0 and 255, the extent or dynamics of the image is 255. PSNR of a color image (RGB) is defined by the equation:

PSNR  10log10

2552  3 MSE  R   MSE  G   MSE  B 

(8)

• The structural similarity index (SSIM): The PSNR measurement gives a numerical value on the damage, but it does not describe its type. Moreover, as is often noted in [20], [21], it does not quite represent the quality perceived by human observers. For medical imaging applications where images are degraded must eventually be examined by experts, traditional evaluation remains insufficient. For this reason, objective approaches are needed to assess the medical imaging quality. We then evaluate a new paradigm to estimate the quality of medical images, specifically the ones

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Before applying wavelet transform on the color image, the RGB color images are converts into YCbCr form, and then applying wavelet transform on each layer independently, this means each layer from YCbCr are compressed as a grayscale image. Fig.5 shows wavelet transform on each YCbCr layer. YCbCr refers to the color resolution of digital component video signals, which is based on sampling rates. In order to compress bandwidth, Cb and Cr are sampled at a lower rate than Y, which is technically known as "chroma subsampling." This means that some color information in the image is being discarded, but not brightness (luma) information. We obtains the best rate of compression using the rich less layer for the chromatic composante Cb and Cr. Y  0.2989 * R  0.5866 * G  0.1145* B  cb  0.1687 * R  0.3312 * G  0.5 * B (11) Cr  0.5 * R  0.4183* G  0.0816 * B 

When the decomposition image is obtained, we try to find a way to code the wavelet transform into an efficient result, taking redundancy and storage space into consideration. After,we apply SPÏHT algorithm on each layer (y,Cr,Cb) independently .

I.J. Information Engineering and Electronic Business, 2014, 2, 28-34

New Contribution on Compression Color Images: Analysis and Synthesis for Telemedicine Applications

C b C r RGB converted to YCbCr

G

RGB color image Apply SPIHT

rate of 0.125 to 2, with a decomposition level (N = 4). The results are shown in fig 5.

Y

R

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B

50

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PSNR (dB)

Apply DWT algorithm on algorithm on each layer each layer Fig 4: Complete steps image compression technique using wavelet independently independently transform (DWT) coupled with SPIHT

This process is repeated for every resolution in the case of level 3 decompositions. The encoding / decoding can be terminated at any time, with the best reproduction obtained up to that point. This is made possible because of the progressive nature of the coding algorithm.

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35 cdf9/7lifting+SPHIT CDF9/7 FB+SPHIT Gall5/3 lifting+ SPHIT CDF 9/7 lifting+ EZW Gall5/3 lifting+ EZW

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VIII. RESULTS AND DISCUSSION

0.95

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MSSIM

We will in this section applied wavelet transform color images on these images contain a lot of data redundancy, we present the performance of different wavelets using two incremental encoders to EZW and SPIHT image compression. The R, G and B of the color image are converted into YCbCr before application of the wavelet transform. Y is the luminance component; Cb and Cr have chrominance components of the image. The image is compressed for the different bits per pixel. Our work is divided into three parts is to make a comparative study between different types of images, Zelda image, Retinal images, and Satellite images and applying the wavelet transform coupled with incremental encoders (EZW, SPIHT) with different filters. For this reason we opted for a set of color images (ZERALDA, RETINAL, and SATELLITE) coded on 24 bits per pixel. For each application we vary sigma value 0.06 to 0.4 and calculate the PSNR and MSSIM. The importance of our work lies in the possibility of reducing the rates for which the image quality remains acceptable. Estimates and judgments of the compressed image quality are given by the PSNR evaluation parameters and the MSSIM similarity Index.

0.85

0.8 CDF9/7lifting+SPHIT CDF9/7 FB+SPHIT Gall5/3 lifting+ SPHIT CDF 9/7 lifting+ EZW Gall5/3 lifting+ EZW

0.75

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b.

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MSSIM Varriation.

Fig 5: Compression results of Zilda image

We note that the metric values increase with the bit rate of 0.125-2 bpp, it is clear that the PSNR values and MSSIM of Gall 5/3 lifting coupled with SPHIT are the best compared to other values. We can say that the Gall5/3 filter lifting is best suited for test images. We are interested in this work to compression of retinal images for this, we chose a retinal image size 512x512 (color) coded 24 bpp registered through retinography. This picture shows a diabetic patient. 55

(a)

(b)

(c)

Fig 1: Popular test images (a) ZELDA, (b) RETINAL, (c) SATELLITE

Here, we adopt test Zilda color image of size 512x512 encoded by 24 bits per pixel for compression algorithm based on wavelet transform coupled with the SPIHT coder with another proposed algorithm (EZW) using different types of filters (cdf 9/7 (filter bank), CDF 9/7 (lifting) Gall5/3 lifting). For each application, we vary the

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PSNR(dB)

50

45

40 cdf l9/7 lifting+SPHIT CDF9/7 FB+SPHIT Gall5/3 lifting + SPHIT CDF 9/7 lifting+EZW Gall5/3 lifting + EZW

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New Contribution on Compression Color Images: Analysis and Synthesis for Telemedicine Applications

We note that wavelets allow us to have the best results with the encoder SPHIT, and PSNR = 51.61dB means high quality of the image after reconstruction. It was a convergence of two curves (CDF Filter Bank) + SPHIT and that of Gall 5/3 lifting + SPHIT but the filter CDF 9/7 (Filter Bank) + SPHIT allows us the best results compared to other filters. To better compare the results obtained by the wavelet compression with the EZW and SPIHT coder for test, retinal and satellite images, we summarize the results in fig 8.

1

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MSSIM

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0.8 cdf l9/7lifting +SPHIT CDF9/7 FB +SPHIT Gall5/3 lifting +SPHIT CDF9/7 lifting +EZW Gall5/3 lifting+ EZW

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Fig 6: Compression results of the retinal image of a diabetic patient 50

PSNR(dB)

We note that the wavelet coupled with SPIHT allow us to have better results and higher PSNR = 51.87dB means good quality image after reconstruction. It was a convergence of two curves (CDF Filter Bank) + SPHIT and that of Gall 5/3 lifting + SPHIT but the filter CDF 9/7 (Filter Bank) + SPHIT allows us the best results compared to other filters. After showing the performance of the wavelet compression to medical images, we now apply our algorithm on the satellite images. To do so, we opted for a satellite image of 512x512 size (color) coded 24 bpp. To investigate the influence of the choice of filter and progressive encoder, we vary the rate of 0.125 to 2bpp, and calculate the evaluation (PSNR, MSSIM) parameters. The results are given in figure.

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Fig 7: Compression results of satellite image

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0.8

1 1.2 Rc(bpp)

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Fig 8: Compression results of the three images (Zelda, retinal and satellite)

Visually, for the three curves it is clear that the algorithm CDF (filter bank) + SPIHT allows us to have a good reconstruction of the image (good compression) so a better image quality, and this is proved by the values major evaluation parameters PSNR = 51.87 the highest value among the PSNR of the other images which shows the effectiveness of our algorithm with the filter CDF 9/7 (filter bank) in the medical field, it means a good quality image after reconstruction. The filter 7 CDF 9 / (Filter Bank) + SPHIT allow us to have the best results compared to other filters.

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IX. CONCLUSION The algorithm that we have implemented can be used in all images; strong performance of our algorithm is not I.J. Information Engineering and Electronic Business, 2014, 2, 28-34

New Contribution on Compression Color Images: Analysis and Synthesis for Telemedicine Applications

only because of the wavelet transform, but also the superiority of the SPIHT coder. Its structure zerotrees allows significant gains in coding cards meaning. The performance of the algorithm on medical images was observed using a retinal gave its performance especially with the CDF (filter bank) filter. REFERENCES [1] M. Nelson, “The data compression book“, 2nded., M&T books, New York, 1996. [2] Said, W.A. Pearlman: An Image Multiresolution Representation for Lossless and Lossy Compression, IEEE Transactions on Image Processing, Vol. 5, No. 9, Sept. 1996, pp. 1303 – 1310. [3] Zandi, J.D. Allen, E.L. Schwartz, M. Boliek: CREW: Compression with Reversible Embedded Wavelets, Data Compression Conference, Snowbird, USA, March 1995, pp. 212 – 221.

Rc: 0.125 bpp PSNR: 31.76 dB MSSIM: 0.75898

Rc: 0.25 bpp PSNR: 36.90 dB MSSIM: 0.88803

Rc: 0.125 bpp PSNR: 31.82 dB MSSIM: 0.65935

Rc: 0.25 bpp PSNR: 39.55 dB MSSIM: 0.85771

Rc: 0.125 bpp PSNR: 30.27 dB MSSIM: 0.67025

Rc: 0.25 bpp PSNR: 35.15 dB MSSIM: 0.84099

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Rc : 0.5 bpp PSNR: 41.43 dB MSSIM: 0.94167

Rc: 0.5 bpp PSNR: 41.16 dB MSSIM: 0.92396

Rc: 0.5 bpp PSNR: 40.57 dB MSSIM: 0.93899

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[4] A.R Calderbank, I. Daubechies, W. Sweldens, B.L. Yeo: Wavelet Transforms that Map Integers to Integers, Applied and Computational Harmonic Analysis, Vol. 5, No. 3, July 1998, pp. 332 – 369. [5] W. Sweldens. The Lifting Scheme: A Custom-design Construction of Biorthogonal Wavelets. Applied and Computational Harmonic Analysis, Vol. 3, No. 2, April 1996, pp. 186 – 200. [6] S.G. Miaou, S.T. Chen, S.N. Chao: Wavelet-based Lossyto-lossless Medical Image Compression using Dynamic VQ and SPIHT Coding, Biomedical Engineering: Applications, Basis & Communications, Vol. 15, No. 6, Dec. 2003, pp. 235 – 242. [7] Mohammed Beladgham, Abdelhafid Bessaid, Abdelmounaim Moulay Lakhdar, Abdelmalik TalebAhmed, Improving Quality of Medical Image Compression Using Biorthogonal CDF Wavelet Based on Lifting Scheme and SPIHT Coding, SERBIAN JOURNAL OF ELECTRICATL ENGINEERING, Vol. 8, No. 2, May 2011, 163-179.

Rc: 0.75 bpp PSNR: 43.92 dB MSSIM: 0.95863

Rc: 1 bpp PSNR: 45.60 dB MSSIM: 0.96971

Rc: 1.5 PSNR: 47.80 dB MSSIM: 0.98116

Rc: 2 bpp PSNR: 49.48 dB MSSIM: 0.98708

Rc: 0.75 bpp PSNR: 46.54 dB MSSIM: 0.96789

Rc: 1 bpp PSNR: 48.02 dB MSSIM: 0.97689

Rc: 1.5 PSNR: 50.20 dB MSSIM: 0.98637

Rc: 2 bpp PSNR: 51.87 dB MSSIM: 0.99141

Rc: 0.75 bpp PSNR: 43.87 dB MSSIM: 0.96554

Rc: 1 bpp PSNR: 46.19 dB MSSIM: 0.97887

Rc: 1.5 PSNR: 49.48 dB MSSIM: 0.98876

Rc: 2 bpp PSNR: 51.61dB MSSIM: 0.99245

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New Contribution on Compression Color Images: Analysis and Synthesis for Telemedicine Applications

Authors’ profiles Mohammed Beladgham was born in Tlemcen, Algeria; he's received the electrical engineering diploma from university of Tlemcen, Algeria, and then a Magister in signals and systems from university of Tlemcen, Algeria and the Ph.D degree in Electronics from the University of Tlemcen (Algeria), in 2012. His research interests are Image processing, Medical image compression, wavelets transform and optimal encoder.

UVHC, His research interests includes signal and image processing. Image segmentation, Prior knowledge integration in image analysis, Partial Differential Equations and Variational Methods in image analysis, Image compression, Multimodal signal processing, Medical image analysis, including multimodal image registration, etc.

Yassine Habchi was born in Mechria, Algeria, received his Bachelor (2005) and Engineers (2010) degree in Electrical Engineering from Saïda University in Algeria, and his Magister (2013) degree in Electronic from university of Bechar , Algeria. His current research interest includes Image processing, Medical image compression, Second generation wavelets and applications and optimal encoder.

A. Moulay Lakhdar he got his Engineering Degree in Telecommunication in 2000 at the Institute of Telecommunications in Oran. Magister was my second degree in Signal and telecom at Djillali LIABES university of Sidi Bel Abbes in 2003. From 2004 to this day I work in the Bechar University as lecturer. Since May 2009, I graduated PhD Es Sciences at the of Sidi Bel Abbes. I do my research at the Bechar University and Communications, Architecture and Media Laboratory (CAMR) (Djillali LIABES University). His research interests are Image transmission, Image processing, and digital transmission performances.

Abdesselam Bassou was born in Bechar, Algeria. He received the Dipl.El.-Ing. Degree from the University of Tlemcen, Algeria in 1997, his Master from the University of Sidi Bel Abbes, Algeria in 2000, and his Doctoral degree Es Science from the University of Sidi Bel Abbes, Algeria in 2006. Actually, He is an Associate Professor at University of Bechar, Algeria. His main interests are digital signal processing, turbo encoding schemes and iterative decoding over fading channels, and channel equalization.

Abdelmaliktaleb-Ahmed Was born in Roubaix, France, in 1962. He received a post graduate degree and a Ph. D. in Electronics and Microwaves from the University of Lille1 in 1988 and 1992. From 1992 to 2004, He was an Associate Professor at the University of Littoral, Calais. Since 2004, He is currently a Professor at the University of Valenciennes in the department GE2I, and does his research at the LAMIH FRE CNRS 3304

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I.J. Information Engineering and Electronic Business, 2014, 2, 28-34

EEA

®

fondată în

1952

Publicaţie trimestrială a consorţiului format din Institutul de Cercetări Electrotehnice al Icpe, Facultatea de Inginerie Electrică din UPB şi Societatea Ştiinţifică Icpe

ISSN 1582-5175

ELECTROTEHNICĂ, ELECTRONICĂ, AUTOMATICĂ

Vol. 62 | nr. 1 | ianuarie–martie 2014

apariţii trimestriale

Scopul revistei Revista EEA îşi propune să publice numai acele articole care, atât prin ideile noi, cât şi prin rezultatele prezentate, să aducă contribuţii importante la cercetarea românească de avangardă, mai ales din electronică, electrotehnică şi automatică. Prezentare Revista EEA a fost fondată în anul 1952 şi are 62 de ani de apariţie neîntreruptă. De-a lungul anilor, deşi a fost unica revistă specializată din domeniul electrotehnicii, EEA a însumat aprecierea a specialiştilor, a cercetătorilor şi a cadrelor didactice din ţară şi din străinătate. +

În prezent, EEA (clasificată B de CNCSIS) este recunoscută, ca lider printre publicaţiile ştiinţifice, pentru calitatea şi standardele înalte ale articolelor apărute în domeniul ştiinţelor inginereşti. Printre autori se numără specialişti din Algeria, Belgia, R.P. China, Finlanda, Franţa, Germania, Italia, Moldova, Slovacia, Ungaria, etc. În paginile revistei, cu apariţii trimestriale, se regăsesc articole, studii, scurte comunicări ce reprezintă contribuţii originale ale celor mai valoroşi specialişti din domeniu, precum şi dezbateri ştiinţifice şi sinteze pe teme prioritare din cercetarea fundamentală şi aplicativă. Principalele rubrici ale revistei sunt:  lucrări ştiinţifice originale (min. 4 pagini–max. 8 pagini),  scurte comunicări (max. 4 pagini),  articole de sinteză (max. 16 pagini),  recenzii / note de lectură ale celor mai recente apariţii de cărţi tehnico-ştiinţifice (max. 1 pagină),  liste de resurse bibliografice comentate, din domeniul ştiinţelor inginereşti (max. 8 pagini). În revistă, pot apărea şi lucrările prezentate la conferinţe, dacă nu au fost publicate (parţial sau integral) în volumul manifestării ştiinţifice respective. Articolele sunt editate preponderent în limba română, dar şi în limbile engleză sau franceză, şi au rezumate şi cuvinte cheie în limbile română şi engleză. Fiecare autor primeşte, gratuit, la cerere, pe suport de hârtie, câte 2 copii ale articolului publicat sau pe suport informatic, în format PDF. Autorii a cel puţin cinci articole publicate în revista EEA, în cursul unui an calendaristic, au reducere la abonamentul din anul calendaristic următor. Revista are un Colegiu ştiinţific internaţional de redacţie format din profesori universitari, cercetători ştiinţifici — personalităţi recunoscute din domeniul ştiinţelor inginereşti (în special din electrotehnică, electronică, automatică etc.). Autorii şi cititorii beneficiază de procedurile riguroase şi imparţiale de lectură şi evaluare (peer review) a propunerilor de articole trimise spre publicare. Acestea sunt recenzate de către experţi specialişti în domeniul lor de activitate, respectiv, al domeniului în care se situează articolul/lucrarea recenzată şi care, fie sunt membri în colegiul de redacţie al revistei, fie sunt din afara acestuia. Procesul de recenzare (peer review), adică de analiză critică a valorii ştiinţifice, este obligatoriu pentru toate manuscrisele trimise spre publicare. Autorilor le revine în exclusivitate responsabilitatea, pentru originalitatea şi exactitatea conţinutului privind exactitatea calculelor, a datelor experimentale şi a afirmaţiilor ştiinţifice prezentate în propunerea de articol. +

Revista EEA este clasificată B de Consiliul Naţional al Cercetării Ştiinţifice din Învăţământul Superior (CNCSIS).

6

ELECTROTEHNICĂ, ELECTRONICĂ, AUTOMATICĂ, vol. 62 (2014), nr. 1 Rolul fizicii în dezvoltarea microelectronicii (Partea 2)

71

(full text in English) Eugen Ştefan LAKATOŞ Abstract The purpose of this paper is to present the basic contributions of Physics in the development of Microelectronics, a science field found at the edge between Physics and Electronics. We will show the road followed by the 20th century science and technique, beginning with 1900, from the rise of quantum theory, elaborated by Max Plank, continuing with the invention of bipolar transistor, up to the manufacturing of the first microprocessor and of the first integrated memory, this way opening the way to the construction of the first personal computer. In this paper, we will present a short review of the main Physics chapters which contributed to the development of the Microelectronics field, of the main theoretical concepts and of physical models which led to the development of the semiconductor devices manufacturing technologies industry. We will present, from the point of view physical phenomena and of modeling, the basic processes in integrated-circuit fabrication: oxidation, epitaxial growth, ion implantation and solid-state diffusion. We will describe the physical models of these processes, models which led to the design of the process flows from Microelectronics industry. These physical models are also used in simulation software of technological processes. For two of the basic processes, oxidation and solid-state diffusion, we will shortly describe the characterization methods, emphasizing once more the role of Physics in Microelectronics field. We will also refer, using examples, to the main process flows used in integrated circuits structures manufacturing that led to the development of Microelectronics.

Eugen Ştefan LAKATOŞ Rezumat Lucrarea îşi propune să prezinte contribuţiile de bază ale fizicii la dezvoltarea Microelectronicii, un domeniu al ştiinţei aflat la graniţa dintre fizică şi electronică. Se punctează drumul parcurs de ştiinţa şi tehnica secolului XX, începând cu 1900, de la apariţia teoriei cuantelor, elaborată de Max Plank, continuând cu inventarea tranzistorului bipolar, până la fabricarea primului microprocesor şi a primei memorii integrate, deschizându-se astfel calea către realizarea calculatorului personal. În lucrare, se prezintă o scurtă trecere în revistă a principalelor capitole ale fizicii care au contribuit la dezvoltarea domeniului Microelectronicii, a principalelor concepte teoretice şi a modelelor fizice care au stat la baza dezvoltării tehnologiilor de fabri-caţie din industria dispozitivelor pe bază de semi-conductori. Sunt prezentate, din punct de vedere al fenomenelor fizice şi al modelării, principalele procese tehnologice care alcătuiesc fluxurile de fabricaţie ale circuitelor integrate: oxidarea, epitaxia, implantarea de ioni şi difuzia. Sunt descrise modelele fizice ale acestor procese, modele ce au stat la baza proiectării fluxurilor tehnologice din industria Microelectronicii. Aceste modele fizice sunt folosite şi în softurile de simulare ale proceselor tehnologice. Pentru două din operaţiile tehnologice, oxidarea şi difuzia, sunt descrise, pe scurt, metodele de caracterizare, evidenţiind şi cu această ocazie, rolul fizicii în domeniul Microelectronicii. De asemenea, se fac referiri, prin exemplificări, la principalele fluxuri tehnologice folosite în fabricaţia structurilor de circuite integrate, care au stat la baza dezvoltării Microelectronicii. Cuvinte cheie: microelectronică, model fizic, proces tehnologic, flux tehnologic

Lămpile fluorescente compacte: o soluţie viabilă încă

The Role of Physics in the Development of Microelectronics (Part 2)

Keywords: microelectronics, physical model, technological process, process flow

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Constantin IVANOVICI, Ionel POPA, Gheorghe GHIUR, Viorel IONESCU Rezumat Specialiştii de la Icpe au realizat noile tipuri de lămpi fluorescente compacte, pentru puteri de 32 W÷105 W cu performanţe îmbunătăţite în ceea ce priveşte randamentul (η), factorul de putere (λ), THDI şi puterea absorbită (Pabs). Au fost proiectate şi realizate noi tipuri de balasturi electronice ce au în componenţă circuite integrate specializate în funcţie de puterea lămpii. Cuvinte cheie: lampă compactă, circuit integrat, balast electronic

Compact Fluorescent Lamps: a Viable Solution even now (full text in Romanian) Constantin IVANOVICI, Ionel POPA, Gheorghe GHIUR, Viorel IONESCU Abstract New types of compact fluorescent lamps of power from 32 W to 105 W with improved performances in terms of: efficiency (η), power factor (λ), total harmonic distortion of the current (THDI) and the absorbed power (Pabs) were performed by specialists of Icpe. New types of electronic ballasts, composed of specialized integrated circuits depending on the nominal power, were designed and manufactured. Keywords: compact lamp, integrated circuit, electronic ballast

MISCELLANEA SECTION O nouă metodă de îmbunătăţire a calităţii vizuale 97 a comprimării imaginii biomedicale folosind transformarea discretă a bandeletei pe baza schemei de ridicare şi codificatorului SPIHT

A Novel Method to improve the Visual Quality of Biomedical Image Compression using Discreet Bandelet Transform based on Lifting Scheme and SPIHT Coder

Mohammed BELADGHAM, Yassine HABCHI, Abdelmouneim Moulay LAKHDAR, Abdesselam BASSOU Rezumat Un sistem de saturaţie pentru depozitare şi transport este o problemă complexă. Această problemă se datorează volumului mare de date. Compresia este una din tehnicile indispensabile pentru rezolvarea acestei probleme. În această lucrare, propunem transformarea bandeletei ca o nouă metodă bazată pe captarea conţinutului geometric complex în imagine. Pentru folosirea acestei transformări pentru studiul şi dezvoltarea algoritmului nostru, am aplicat această tehnică pe diferite tipuri de imagini comprimate (naturale, medicale şi imagini din satelit) folosind transformarea bandeletei cuplată cu două tipuri de codificatoare performante (EZW şi codificatorul SPIHT). Scopul acestei lucrări este de a examina capacitatea acestei transformări care să ofere o

(full text in English) Mohammed BELADGHAM, Yassine HABCHI, Abdelmouneim Moulay LAKHDAR, Abdesselam BASSOU Abstract A saturation system of storage and transmission is a complex problem. This problem is due to the large volume of data. Compression is one of the indispensable techniques to solve this problem. In this work, we propose bandelet transform as a new method based on capturing the complex geometric content in image. To use this transform to study and develop our algorithm, we have applied this technique on different types of compressed images (natural, medical and satellite images) using the bandelet transform coupled by two types performing coders (EZW and SPIHT coder). The goal of this paper is to examine the capacity of this transform proposed to offer an optimal representation for image geometric. Being interested in compressed medical image, in order to

A Novel Method to improve the Visual Quality of Biomedical Image Compression using Discret Bandelet Transform based on Lifting Scheme and SPIHT Coder Mohammed BELADGHAM, Yassine HABCHI, Abdelmouneim Moulay LAKHDAR, Abdesselam BASSOU ∗ Abstract A Saturation storage and transmission system is a very complex problem, this problem is from large volume of data. Compression is one of the indispensable techniques to solve this problem. In this work, we propose bandelet transform is a new method based on capturing the complex geometric content in image; we use this transform to study and develop our algorithm, for this we have applied this technique on different types of images natural, medical and satellite images compressed using the bandelet transform coupled by two types performant coder (EZW and SPIHT coder). The goal of this paper is to examine the capacity of this transform proposed to offer an optimal representation for image geometric. We are interested in compressed medical image, In order to develop the compressed algorithm we compared our results with those obtained by the bandelet transform application in satellite image field. We concluded that the results obtained are very satisfactory for medical image domain. Keywords: bandelet transform, lifting scheme optical flow, quadtree segmentation, SPIHT and EZW coder

1. Introduction Today, the diagnostic medical system at distance, digital library and Internet are applied popularly. One of the most important problems in such applications is how to store and transmit images [1]. The medical diagnostic field is interested by the researchers. It is well established that the accuracy and precision of diagnostic are initially related to the image quality. Finding the efficient geometric representations of images is a central issue in improving the efficiency of image compression. Many ideas have already been studied to find new bases can capture geometric regularity image. Image representations in separable orthonormal bases such as Fourier, local Cosine or Wavelets can not take advantage of the geometrical regularity of image structures. Standard wavelet bases are optimal to represent functions with piecewise singularities. ∗

Mohammed BELADGHAM: PhD., Department of Electronic, Bechar University,POBox 417, 08000, Bechar, Algeria, [email protected] Yassine HABCHI: Eng., Department of Electronic, Bechar University,POBox 417, 08000, Bechar, Algeria, [email protected] Abdelmouniem Moulay LAKHDAR: PhD., Department of Electronic, Bechar University,POBox 417, 08000, Bechar, Algeria, [email protected] Abdesselam BASSOU: Associate Professor, Department of Electronic, Bechar University,POBox 417, 08000, Bechar, Algeria, [email protected]

However, they fail to capture the geometric regularity along the singularities of edges or contours because of their isotropic support. To exploit the anisotropic regularity along edges, the basis must include elongated functions that are nearly parallel to the edges. Multiscale geometric analysis (MGA) developed recently provides a group of new basis that has anisotropic supports such as Curvelets [2-7]. A Curvelet frame is composed of multiscale elongated and related wavelet type functions, for this reason, In this paper, we introduce a new type of transform, called bandelet transform by E. Le Pennec and Stéphane Mallat [8]. This transform is the most recently developed method of compression technique, which decompose the image along multiscale vectors that are elongated in the direction of a geometric flow. This geometric flow indicates directions, in which the image gray levels have regular variations; bandelet bases can represent the geometric regular images efficiently. 2. The Bandelet Transform Bandelet transform, introduced by Le Pennec and Mallat [9] built a base adapted to the geometric content of an image. The bandelets are obtained from a local deformation of space to align the direction of regularity with a fixed direction (horizontal or vertical) and is reduced to a separable basis [10], [11] (see Figure 1).

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segmentation is the following: Start

Read the input image N*N Figure 1. Deformation of horizontal field according to a geometric flow

Step quadtree decomposition T

2.1. Flow-curve relationship There is a constant correspondence among the flow along the vertical direction and curves whose tangent is never vertical; the flow associated with this curve is given by flow: 1  τ( x ) =  ′  2 1 + c′( x)  c ( x)  1

L ( f , R, B ) = f − f R

Stopping test:

No

~ LL

(1)

where c ' (x ) : Slope of optical flow. We can generate the basic test bandelet according to the flow and geometric regularity of each sub-block. If there is no flow geometry in the sub-blocks, this means that the sub-block is uniformly regular, so that we can use the classical separable wavelet basis for treating this sub-block. If not, the sub-block must be processed by the bandelet. If the sub-block is not uniformly regular, we can deform it, has variation along geometric flow defined in the sub-block [12]. For have the sub-block that contains the singularity that is with a calculation of Lagrangian [13]. 2

Decomposition

+ λ.T 2 ∑ R jG + R jB j

(

)

(2)

Yes Save decomposition

End Figure 3. Segmentation quadtree diagram functional

For have the optimal segmentation that is with [14]:

{

}

L0 ( S ) = min L0 ( S ) , L ( S )

(3)

where: L ( S ) = L0 ( S1 ) + L0 ( S2 ) + L0 ( S3 ) + L0 ( S4 ) + L0 ( S ) +λ.T 2

L0 ( Si ) : Lagrangian of sub-blocks.

2.3. The operator of deformation The deformation operation is a local operation on a block that contains a curve singularity to align or correct in a direction horizontal and vertical.

where:λ: Lagrangian; T: Quantifiction step; RjG: is the number of bits to code the optical flew in each square; RjB: is the number of bits to code the quantized bandelet coefficients. 2.2. Quadtree segmentatin The segmentation operation is a successive division of image space that allows us to have a set of sub-blocks.

a)

c)

Figure 2. Example of quadtree segmentation

The operating diagram of the quadtree

b)

d)

Figure 4. Example of model horizon and deformation of the field according to a geometric flow. Image distortion: a) an image having a horizontal flow, b) its image by the operator W, c) an image having a vertical flow, d) the image by the operator W

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The deformation operation gives a wavelet orthonormal basis of L2(Ω):  ϕ j , n ( x1 ) ψ j , n ( x 2 − c ( x1 ))  1 2    ψ j , n1 ( x1 ) ϕ j , n 2 ( x 2 − c ( x1 ))     ψ j , n1 ( x1 ) ψ j , n 2 ( x 2 − c ( x1 )) 

(4)

The horizontal wavelet ψ Hj,n has not vanishing moments along contour, to be replaced by new functions: ψ l , n1 ( x1 ) ψ j , n2 ( x2 − c( x1 ))

(5)

This is called bandeletization [15], [16]. The orthonormal basis of bandelet of field warping is defined by:  ψl , n ( x1 )ψ j , n ( x2 − c( x1 ))  ψlH, n  2  1    ψ ( x ) ϕ  j ,n1 1 j , n2 ( x2 − c( x1 ))  = ψVj ,n  j, l > n1 , n2    D   ψ j ,n1 ( x1 )ψ j , n2 ( x2 − c( x1 ))  ψ j , n 

determine the maximum value of the wavelet coefficients, so in the first dominant pass, if the coefficient absolute value is greater than the threshold, so we obtained a positive code or negative code according to the sign of coefficient, if the absolute value is less, we check the descendants coefficient, if you have a coefficient with absolute value above the threshold, we obtained IZ code, else we have a code ZT. In the second pass, the comparison is made in the middle of the interval [Tn, 2Tn], if this coefficient belongs to the first interval, so we are a transmission of the bit 1, if this coefficient belongs to the second interval, so there are a transmission of bit 0. 5. SPIHT Coding Scheme

(6)

3. Operational diagram Start

2D Image

The SPIHT algorithm proposed by Said and Pearlman in 1996 [18], ameliorate progressive algorithm is compared to the EZW algorithm, based on the creation of three list SCL, ICL and ISL with a calculated threshold T, each time you make a scan on both lists SCL and ISL and that for the classified the significant coefficient in the list of significant coefficient. 6. Quality Evaluation parameter

2D- Wavelet transform

Optical flow

The Peak Signal to Noise Ratio (PSNR) is the most commonly used as a measure of quality of reconstruction in image compression. The PSNR were identified using the following formulate:

Quadtree segmentation

MSE =

Is this-that the sub-square is regular?

∧ 1 M −1 N −1   . ∑ ∑  I ( i, j ) − I ( i, j ) M .N i = 0 j = 0  

No Warping +Bandeletization

End

Figure 5. Bandelet transform operational diagram

4. EZW Coding Scheme The algorithm proposed by Shapiro [17], the design of this algorithm is based on two pass with a calculated threshold T, we

(7)

Mean Square Error (MSE) which requires two MxN gray scale images I and Î, where one of the images is considered as a compression of the other, is defined as: − The PSNR is defined as: PSNR = 10.log10

Yes

2

(2

R

− 1)

MSE

2

[ dB ]

(8)

The structural similarity index (SSIM): The PSNR measurement gives a numerical value on the damage, but it does not describe its type. Moreover, as is often noted in [20], [21], it does not quite represent the quality perceived by human observers. For medical imaging applications where images are degraded must eventually be examined by experts, traditional evaluation remains insufficient. For this reason, the objective approaches are needed to assess the medical −

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imaging quality. We then evaluate a new paradigm to estimate the quality of medical images, specifically the ones compressed by wavelet transform, based on the assumption that the human visual system (HVS) is highly adapted to extract structural information. The similarity compares the brightness, contrast and structure among each pair of vectors, where the structural similarity index (SSIM) between two signals x and y is given by the following expression:

SSIM ( x, y ) = l ( x, y ) c ( x, y ) s ( x, y )

( )

M

∑ SSIM ( I , Iˆ ) i

(10)

i

e) Figure 6. Examples of sets of images: a) LINA; b) MRI; c) CT; d) ECHO and e) TOREX original images

i =1

where: I and Î are, respectively, the reference and degraded images, Ii and Îi are the contents of images at the i-th local window; M: the total number of local windows in image. The MSSIM values exhibit greater consistency with the visual quality. 7. Results and Discussion We are interested in this work to the medical images compression, that we applied algorithm (DBT+SPIHT), (DBT+EZW). For this, we chose sets of medical images (MRI, CT, ECHO and TOREX) images gray level size 512x512 encoded on 8 bits per pixel. These images are taken from the GE Medical System (database) [21]. The importance of our work lies in the possibility of reducing the rates, for which the image quality remains acceptable. Estimates and judgments of the compressed image quality are given by the PSNR evaluation parameters and the MSSIM similarity Index.

a)

d)

(9)

Finally, the quality measurement can provide a spatial map of the local image quality, which provides more information on the image quality degradation, which is useful in medical imaging applications. For application, we require a single overall measurement of the whole image quality that is given by the following formula: 1 MSSIM I , Iˆ = M

c)

b)

In this section, we applied the bandelet transform on these images thatcontain a lot of data redundancy; we present the performance of different filters using two incremental encoders to EZW and SPIHT image compression. The image is compressed for the different bits per pixel. Our work is divided into two parts is to make a comparative study among different filters types for MRI image and applying after a filter how permit us to have a important value of PSNR to the sets of images (LINA, CT, ECHO, TOREX and SATELLITE) images gray level size 512x512 encoded on 8 bits per pixel. For each application, we vary the rate of 0.25 to 2 values and calculate the PSNR and MSSIM. To show the performance of the proposed method, we made a comparison among these different types of transform: (DBT+CDF9/7(Lift)+EZW); (DBT+GALL5/3(Lift)+EZW), (DBT+CDF9/7+EZW) and (DBT+GALL5/3+EZW) coupled with the EZW coding. For each application we varied the bit-rate 0.25 to 2, and we calculated the PSNR and MSSIM. We chose the MRI image gray level size 512x512 encoded on 8 bits per pixel. The results obtained are given in Table 1 and Figure 7.

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Table 1. PSNR and MSSIM variation using bandelet transform coupled by EZW coder (MRI) Rc (bpp)

DBT+CDF9/7(Lift)+EZW PSNR(dB) MSSIM 20.2649 0.7130 31.7018 0.8436 34.9082 0.8855 37.2096 0.9051 39.8667 0.9231 41.5950 0.9321

0.25 0.5 0.75 1 1.5 2 45

DBT+GALL5/3(Lift)+EZW PSNR(dB) MSSIM 20.3109 0.7228 27.7312 0.8304 34.6760 0.8873 36.5688 0.9035 38.5410 0.9162 40.6542 0.9271 1

DBT+CDF9/7(Lift)+EZW DBT+GALL5/3(Lift)+EZW DBT+CDF9/7+EZW DBT+GALL5/3+EZW

40

DBT+CDF9/7+EZW PSNR(dB) MSSIM 19.4174 0.6237 27.0976 0.7449 29.0929 0.7859 32.0735 0.8293 36.5894 0.8876 38.2037 0.9059

DBT+GALL5/3+EZW PSNR(dB) MSSIM 20.2788 0.6904 26.9801 0.8152 34.5209 0.8877 36.4461 0.9030 38.5948 0.9170 40.6733 0.9274

DBT+CDF9/7(Lift)+EZW DBT+GALL5/3(Lift)+EZW DBT+CDF9/7+EZW DBT+GALL5/3+EZW

0.95 0.9 0.85 MSSIM

PSNR(dB)

35

30

0.8 0.75

25

0.7 20

0.65 15 0.2

0.4

0.6

0.8

1 1.2 Rc(bpp)

1.4

1.6

1.8

2

0.2

0.4

0.6

0.8

1 1.2 Rc(bpp)

a)

1.4

1.6

1.8

2

b)

Figure 7. Numerical results PSNR and MSSIM of compression MRI image by bandelet transform coupled with EZW coder: a) PSNR results; b) MSSIM results

Visually, from the curves, We note that the (DBT+CDF9/7(LIFT)) coupled with EZW allow us to have better results (good image reconstruction) so a better image visual quality and this is proved by higher PSNR = 41.5950 dB value for 2bpp, this means good quality image after reconstruction.

In order to evaluate PSNR results, we opted to other coder type named ‘SPIHT coder’, we use this type for compression MRI image gray level size 512x 512 encoded on 8 bits per pixel. This image is taken from the GE Medical System database [21]. The results are showed in Table 2 and Figure 8.

Table 2. PSNR and MSSIM variation using bandelet transform coupled by SPIHT (MRI) Rc (bpp) 0.25 0.5 0.75 1 1.5 2

DBT+CDF9/7(Lift)+SPIHT PSNR(dB) MSSIM 19.9803 0.6988 30.9730 0.8382 34.7835 0.8872 37.3675 0.9077 41.1318 0.9299 44.8086 0.9453 45

40

DBT+GALL5/3(Lift)+SPIHT PSNR(dB) MSSIM 20.0348 0.7087 29.1376 0.8302 34.4845 0.8876 36.8521 0.9058 40.1170 0.9239 43.0328 0.9384

DBT+CDF9/7+SPIHT PSNR(dB) MSSIM 19.5678 0.6536 27.1325 0.7452 31.5515 0.8206 34.1964 0.8639 38.9237 0.9102 42.8200 0.9437

DBT+GALL5/3+SPIHT PSNR(dB) MSSIM 19.8343 0.6770 26.8793 0.8156 34.4376 0.8866 36.8161 0.9064 40.0500 0.9240 42.7707 0.9374

1

DBT+CDF9/7(Lift)+SPIHT DBT+GALL5/3(Lift)+SPIHT DBT+CDF9/7+SPIHT DBT+GALL5/3+SPIHT

0.95

DBT+CDF9/7(Lift)+SPIHT DBT+GALL5/3(Lift)+SPIHT DBT+CDF9/7+SPIHT DBT+GALL5/3+SPIHT

0.9

MSSIM

PSNR (dB)

35

30

25

0.8

0.75

20

15 0.2

0.85

0.7

0.4

0.6

0.8

a)

1 1.2 Rc(bpp)

1.4

1.6

1.8

2

0.65 0.2

0.4

0.6

0.8

1 1.2 Rc(bpp)

1.4

1.6

1.8

2

b)

Figure 8. Numerical results PSNR and MSSIM of compression MRI image by bandelet transform coupled with SPIHT coder: a) PSNR results; b) MSSIM results

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By comparing the different values of PSNR and MSSIM, we note that (DBT+CDF9/7(LIFT)) coupled with SPIHT allow us to have better results compared to other filters and higher PSNR = 44.8086 dB means good quality image after reconstruction. In the following, we DBT+CDF9/7(LIFT)+EZW

Rc= 0.25

Rc= 0.5

present the compressed MRI images quality for different bit-rate values (number of bits per pixel) by (DBT + SPIHT) algorithm for different methods Rc=0.75

Rc=1

Rc=1.5

Rc=2

DBT+GALL5/3(LIFT)+EZW

DBT+CDF9/7+EZW

DBT+GALL5/3+EZW

DBT+CDF9/7(LIFT)+SPIHT

DBT+GALL5/3(LIFT)+SPIHT

DBT+CDF9/7+SPIHT

DBT+GALL5/3+SPIHT

Figure 9. Compressed MRI images by DBT + SPIHT algorithm for different methods

After showing the performance of the algorithm (DBT+CDF9/7(LIFT) coupled with SPIHT) for MRI image. Now, in this study, we subsequently generalize and apply our algorithm to the sets of images of the GE Medical Systems Database (LINA, CT, ECHO, TOREX and satellite), in order to specify the type of image adapted to the algorithm.

To investigate the influence of the choice of filter and progressive encoder, we present the results of compression images obtained after application of our algorithm. These results are obtained with a 0.75 bpp bite-rate and calculate the evaluation (PSNR, MSSIM) parameters. The results are given in Figure 10.

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ELECTROTEHNICĂ, ELECTRONICĂ, AUTOMATICĂ, vol. 62 (2014), nr. 1

PSNR=38.9047 MSSIM=0.9427

PSNR=39.9304 MSSIM=0.9615

PSNR=39.6424 MSSIM=0.9635

PSNR=45.4014 MSSIM=0.9833

PSNR=29.5608 MSSIM=0.8533 Figure 10. Compressing of different images by bandelet transform using CDF9/7 (Lifting scheme) and SPIHT coding for 2bpp

According to the PSNR and MSSIM values, we note that from (DBT+CDF9/7(LIFT)), TOREX image reconstruction becomes almost perfect, and better than to the others images. 8. Conclusions Medical image compression using the bandelet transform is still a vast research field. These transform provides a very compact representation of images and can capture more chaotic geometries and a major improvement compared to other transforms. We used the Biorthogonal CDF9/7 compression based on lifting scheme, coupled with the SPIHT coding. After several applications, we found that this algorithm gives better results than the other compression techniques for TOREX image. Thus, we conclude that the results obtained are very satisfactory in terms of compression ratio and compressed image quality. However, research in this domain is still in its beginning and the current obtained results are difficult to evaluate. In the future we are going to work into defining a strategy to exploit the bandelet transform for color image compression. 9. References [1] Nelson M., The Data Compression Book. 2nd ed., M&T books, New York, 1996. [2] Starck J.L., Murtagh F., Candès E., and Donoho D.L., “Gray and Color Image Contrast Enhancement by the Curvelet Transform”. in IEEE Transaction on Image

Processing, Vol. 12, No. 6, pp 706-717, 2003. [3] Candès U.E.J. and Donoho D.L., “New Tight Frames of Curvelets and Optimal Representations of Objects with Piecewise C2 Singularities”, in Comm. on Pure and Appl. Math. Vol. 57, pp.219-266, 2004. [4] Do M.N. and Vetterli M., Contourlets, Beyond Wavelets (J. Stoeckler and G.V. Welland, Eds.) San Diego, CA: Academic Press, 2003. [5] Romberg K., Wakin M.B., and Baraniuk R.G., “Approximation and Compression of Piecewise Smooth Images Using a Wavelet/Wedgelet Geometric Model”. In IEEE 2003 International Conference on Image Processing - ICIP-2003, Barcelona, Spain, September 2003. [6] Borup L. and Morten N., “Approximation with Brushlet Systems”, in Journal of Approximation Theory. Vol. 123, pp. 25-51, 2003. [7] Velisavljevici V., Beferull-Lozano B., Vetterli M. and Dragotti P.L., “Directionlets: Anisotropic Multidirectional Representation with Separable Filtering”. in IEEE Trans. Image Processing, Dec, 2004. [8] Le Pennec E., Mallat S., “Bandelet Representation for Image Compression”. In Proc. Int. Conf. Image Processing, Oct. 2001. [9] Le Pennec E., Mallat S., “Représentation d’images par bandelettes et application à la compression”, in GRETSI, Toulouse, Septembre 2001. [10] Le Pennec E., Bandelettes et représentation géométrique des images. thèse de Doctorat, Ecole Polytechnique, 19 déc. 2002.

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[11] Chappelier V., Codage progressif d'images par ondelettes orientées. Thèse de Doctorat, Université Rennes 1, 15 déc. 2005. [12] Ding. Time Frequency Analysis Tutorial. R99942057. [13] Hong Han, Xing Wu. Research of Method in Human Detection based on Bandelet Transform in Laboratory of Intelligent Perception and Image, Understanding of Ministry of Education of China, Vol. 74951S, 2009. [14] Ruihua Liang, Lizhi Cheng, Zhicheng Zhu, Bo Chen. “Image Coding based on Second Generation Bandelet Transform”. in Modern Electronics Technique, 61-65 (2007). [15] Le Pennec E., Mallat S., Bandelettes et représentation géométrique des images. CMAP/Ecole Polytechnique, 91128 PALAISEAU, France. [16] Le Pennec E., Mallat S., Bandelet Representations for Image Compression. 0-7803-6725-1/01. IEEE. 2001. [17] SHAPIRO J., “Embedded Image Coding using Zerotree of Wavelet Coefficients”. in IEEE Trans. Signal Processing. Vol. 41, pp. 3445-3462. Dec, 1993. [18] Said A. and Pearlman W.A., “A New and Efficient Image Codec based on Set Partitioning in Hierarchical Trees”. in IEEE Transactions on Circuits and Systems for Video Tech., vol. 6, pp. 243–250, 1996. [19] Geisler W.S., Banks M.S., Visual Performance: Handbook of Optics, Vol. 1, McGraw-Hill, NY, USA, 1995. [20] Watson A.B., Kreslake L.B., “Measurement of Visual Impairment Scales for Digital Video”. in Human Vision and Electronic Imaging Conference, San Jose, CA, USA, SPIE Vol. 4299, Jan. 2001, 2001, pp. 79–89. [21] www.GE Medical System.com (database).

10. Biography Mohammed BELADGHAM was born in Tlemcen, Algeria; he's received the electric engineering diploma from university of Tlemcen, Algeria, and then a Magister in signals and systems from university of Tlemcen Algeria and the Ph.D. degree in Electronics from the University

of Tlemcen (Algeria), in 2012. His research interests are Image processing, Medical image compression, wavelets transform and optimal encoder. Yassine HABCHI was born in Mechria, Algeria, received his Bachelor (2005) and Engineers (2010) degree in Electric Engineering from Saïda University in Algeria, and his Magister (2013) degree in Electronic from University of Bechar, Algeria. His current research interest includes Image processing, Medical image compression, wavelets transform and optimal encoder. A. Moulay LAKHDAR got my Engineering Degree in Telecommunication in 2000 at the Institute of Telecommunications in Oran. Magister was my second degree in Signal and telecom at Djillali LIABES university of Sidi Bel Abbes in 2003. From 2004 to this day I work in the Bechar University as lecturer. Since May 2009, I graduated PhD Es Sciences at the of Sidi Bel Abbes. I do my research at the Bechar University and Communications, Architecture and Media Laboratory (CAMR) (Djillali LIABES University). His research interests are Image transmission, Image processing, and digital transmission performances. Abdesselam Bassou was born in Bechar, Algeria. He received the Dipl.El.-Ing. Degree from the University of Tlemcen, Algeria in 1997, his Master from the University of Sidi Bel Abbes, Algeria in 2000, and his Doctoral degree Es Science from the University of Sidi Bel Abbes, Algeria in 2006. Actually, He is an Associate Professor at University of Bechar, Algeria. His main interests are digital signal processing, turbo encoding schemes and iterative decoding over fading channels, and channel equalization.

I.J. Image, Graphics and Signal Processing, 2014, 3, 43-50 Published Online February 2014 in MECS (http://www.mecs-press.org/) DOI: 10.5815/ijigsp.2014.03.06

A Comparative Study between X_Lets Family for Image Denoising Beladgham Mohamed1, Habchi Yassine2, Moulay Lakhdar Abdelmouneim3, Abdesselam Bassou4 , Taleb-Ahmed Abdelmalik5 1

University of Bechar, Algeria, Department of Electronic, Faculty of Sciences and Technology, Postal address, 08000, Bechar, Algeria, E-Mail: [email protected] 2

University of Bechar, Algeria, Department of Electronic, Faculty of Sciences and Technology, Postal address, 08000, Bechar, Algeria, E-Mail: [email protected] 3

University of Bechar, Algeria, Department of Electronic, Faculty of Sciences and Technology, Postal address, 08000, Bechar, Algeria, E-Mail: [email protected] 4

University of Bechar, Algeria, Department of Electronic, Faculty of Sciences and Technology, Postal address, 08000, Bechar, Algeria, E-mail: [email protected] 5

Biomecanic Laboratory, Valencienne University, France 59313, Valenciennes, Francia, E-Mail: [email protected]

Abstract Research good representation is a problem in image processing for this, our works are focused in developing and proposes some new transform which can represent the edge of image more efficiently, Among these transform we find the wavelet and ridgelet transform these both types transforms are not optimal for images with complex geometry, so we replace this two types classical transform with other effectiveness transform named bandelet transform, this transform is appropriate for the analysis of edges of the images and can preserve the detail information of high frequency of noisy image. De-noising is one of the most interesting and widely investigated topics in image processing area. In order to eliminate noise we exploit in this paper the geometrical advantages offered by the bandelet transform to solve the problem of image de-noising. To arrive to determine which type transform allows us high quality visual image, a comparison is made between bandelet, curvelet, ridgelet and wavelet transform, after determining the best transform, we going to determine which type of image is adapted to this transform. Numerically, we show that bandelet transform can significantly outperform and gives good performances for medical image type TOREX, and this is justified by a higher PSNR value for gray images. Index Terms Bandelet transform, Contourlet transform, Curvelet transform, Ridgelet transform, Quadtree segmentation.

Copyright © 2014 MECS

I. INTRODUCTION Image de-noising is one of the most popular research fields in image processing due to the fact that it is extremely difficult to form a general global de-noising scheme effective for all types of noise as well as all types of images. A common problem in image denoising is the blurring of the prominent edges in the image which can cause discrepancies when the denoising operation is combined with other operations such as image edge detection and segmentation. For image de-noising processing many classical methods can be applied to de-noise, such as wavelet has become a useful tool for analysis of many kinds of problems, wavelets are good at catching point singularities, but for linear singularity, wavelets transform cannot capture well. To overcome the weakness of wavelets in higher dimensions, Candes and Donoho [1] pioneered a new system of representations named ridgelets which they showed to deal effectively with line singularities in 2D, ridgelet [2] is a new perfect tool to analyze and synthesize the 2-dimensional and the high-dimensional singularities. In the recent years, S.Mallat and E.Le Pennec proposed new transform named bandelet transform [3] construct a basis with a multiscale geometry adapted to image, can capture directional geometric image regularity and provide an optimal approximation for a more complex class of geometric images.

I.J. Image, Graphics and Signal Processing, 2014, 3, 43-50

44

A Comparative Study between X_Lets Family for Image Denoising

opt

 arg min L f , , T 

(3)

II. BANDELET TRANSFORM Bandelet transform, introduced by E. Le Pennec and S. Mallat [4] built a base adapted to the geometric content of an image. The bandelets are obtained from a local deformation of space to align the direction of regularity with a fixed direction (horizontal or vertical) and is reduced to a separable basis [5].

Then the corresponding 1D wavelet coefficients to

opt

t is defined as bandelet coefficients and the

optimal direction image. [7]

opt

t is recorded for reconstructing

B.

QUADTREE SEGMENTATION Segmentation operation it is a division of image space that allows us to have a set of sub-blocks.

Figure 1. Example of model horizon and deformation of the field according to a geometric flow

A.

FLOW-CURVE RELATIONSHIP There is a constant correspondence between the flow along the vertical direction and curves whose tangent is never vertical; the flow associated with this curve is given by flow: ( x) 

1 c ( x)

1 1  c ( x)

2

Figure 2. Example of quadtree segmentation

The operating diagram of the quadtree segmentation is the following. Start

(1)

Read the input image N*N

c '  x  : Slope of optical flow.

Step quadtree decomposition T

We can generate the basic test bandelet according to the flow and geometric regularity of each sub-block. If there is no flow geometry in the sub-blocks, this means that the sub-block is uniformly regular so that we can use the classical separable wavelet basis for treating this sub-block. If not, the sub-block must be processed by the bandelet. Also, the variation along geometric flow defined in the sub-block means that we can deform the sub-block in horizontal or vertical direction, in this case we can say that the sub-block is uniformly regular. Calculates the Lagrangian allows us to determine subblock that contains the singularity [6]. L f , R, B   f  f R

2

 .T

2

 R jG  R jB 

Stopping test:

No

~ L  L

Yes Save decomposition

End

Figure 3. Segmentation quadtree diagram

The optimal segmentation is defined with [8]: (2)

j

: Lagrangian multiplier. T : Quantifiction step. R jG : is the number of bits to code the optical flew in each square. R jB : is the number of bits to code the quantized bandelet coefficients. f R : is the reconstructed 1D signal by thresholding the coefficients smaller than T . The optimal direction in each dyadic sub-region can be defined as Copyright © 2014 MECS

Decomposition





~ L0 S   min L0 S , L S 

(4)

Where ~ L S   L0 S1   L0 S 2   L0 S 3   L0 S 4   L0 S   .T 2 L0 Si 

(5)

: Lagrangian of sub-blocks.

C.

THE OPERATOR OF DEFORMATION The deformation operation is a local operation on a block that contains a curve singularity to align or correct in a direction horizontal and vertical. I.J. Image, Graphics and Signal Processing, 2014, 3, 43-50

A Comparative Study between X_Lets Family for Image Denoising

45

function , the same construction gives a biorthogonal 2 basis of L ( ) .

(a)

(b)

III. DIAGRAM OF OPERATION Start

(c)

2D Image

(d)

2D- Wavelet transform

Figure 4. Segmentation Example of model horizon and deformation of the field according to a geometric flow. Image distortion: (a) an image having a horizontal flow, (b) its image by the operator W, (c) an image having a vertical flow, (d) the image by the operator W

Optical flow

Quadtree segmentation

Note that the two-dimensional Wavelet basis is:

    

j ,n1 ( x1 )

j ,n2 ( x2 )

j ,n1 ( x1 ) j ,n2 ( x2 )



Is this-that the sub-square is regular?

(6)

 j ,n1 ( x1 ) j ,n2 ( x2 ) 

Yes No

Deformation operation gives a wavelet orthonormal

Warping +Bandeletization

2 basis of L ( ) :

    

j , n1 ( x1 ) j , n1 ( x1 )

End

j , n 2 ( x2 j , n2

 c( x1 ))

( x2  c( x1 ))

Figure 5. Bandelet transform operation diagram



(7)

 j , n1 ( x1 ) j , n 2 ( x2  c( x1 )) V j,n

IV. QUALITYEVALUATION PARAMETER D j,n

The vertical and diagonal Wavelets have vanishing moments along contour, they are therefore suitable for the approximation of function f is regular along contour is not the case of horizontal wavelet to be replaced by new functions: l , n1 ( x1 )

j , n2

( x2  c( x1 ))

H j,n

,

(8)

This is called bandeletization and we check it is implemented by a simple 1D discrete Wavelet transform [9], [10]. The orthonormal basis of bandelet of field warping is defined by:   j ,n1 ( x1 ) j ,n2 ( x 2  c( x1 ))    j ,n1 ( x1 ) j ,n2 ( x 2  c( x1 )) 

l ,n1 ( x1 ) j ,n2 ( x 2

 c( x1 ))

H l ,n



V  j ,n D  j ,n 

j, l n1 , n2

(9)

The orthogonality property is not sufficient; we take the bandelet dimensional biorthogonal and its scaling

Copyright © 2014 MECS

The Peak Signal to Noise Ratio (PSNR) is the most commonly used as a measure of quality of reconstruction in image compression. The PSNR were identified using the following formulate: MSE 

  1 M 1N 1 .    I i, j   I i, j  M .N i  0 j  0  

2

(10)

Mean Square Error (MSE) which requires two MxN gray scale images I and Iˆ where one of the images is considered as a compression of the other is defined as: The PSNR is defined as: PSNR  10. log 10

2  1 R

MSE

2

dB 

(11)

Usually an image is encoded on 8 bits. It is represented by 256 gray levels, which vary between 0 and 255, the extent or dynamics of the image is 255. The structural similarity index (SSIM): The PSNR measurement gives a numerical value on the damage, but it does not describe its type. Moreover, as is often noted in [11], [12], [13], it does not quite I.J. Image, Graphics and Signal Processing, 2014, 3, 43-50

46

A Comparative Study between X_Lets Family for Image Denoising

represent the quality perceived by human observers. For medical imaging applications where images are degraded must eventually be examined by experts, traditional evaluation remains insufficient. For this reason, objective approaches are needed to assess the medical imaging quality. We then evaluate a new paradigm to estimate the quality of medical images, specifically the ones compressed by wavelet transform, based on the assumption that the human visual system (HVS) is highly adapted to extract structural information. The similarity compares the brightness, contrast and structure between each pair of vectors, where the structural similarity index (SSIM) between two signals x and y is given by the following expression:

SSIM x, y   l x, y cx, y sx, y 

V. RESULTS AND DISCUSSION In this article, we give numerical experiments to test our denoising method. For this reason we opted for a set of medical images (MRI, CT, ECHO and TOREX) gray scale coded on 8 bits per pixel. These images are taken from the GE Medical System (database) [15]. The importance of our work lies in the possibility of reducing the noise for which the image quality remains acceptable. Estimates and judgments of the de-noised image quality are given by the PSNR evaluation parameters and the MSSIM similarity Index. For each application we vary sigma value 0.06 to 0.4 and calculate the PSNR and MSSIM. The results obtained are given in Table1 and Table2.

(12)

Finally the quality measurement can provide a spatial map of the local image quality, which provides more information on the image quality degradation, which is useful in medical imaging applications. For application, we require a single overall measurement of the whole image quality that is given by the following formula:

 

1 MSSIM I , Iˆ  M

 SSIM I i , Iˆi  M

(13)

CORRELATION COEFFICIENT (CC) The correlation coefficient, r , is widely used in statistical analysis, and image processing for compared two images of the same object (or scene). The r value indicates whether the object has been altered or moved. The correlation coefficient is defined as

TABLE 1. NUMERICAL RESULTS OBTAINED AFTER MRI IMAGE DE-NOISING FOR T=10 AND T=30 0.06

0.08

0.1

0.4

PSNR (dB)

29.86 66

28.1657

26.841 8

17.484 6

MSSIM

0.783 5

0.7405

0.7158

0.4784

PSNR (dB)

31.25 75

29.5726

28.085 9

18.031 4

MSSIM

0.812 6

0.7783

0.7503

0.5214

(14) STEP (T)

i

xi

is the intensity of the ith pixel in image 1,

is the intensity of the ith pixel in image 2,

mean intensity of image 1, and of image 2.

ym

xm

T=10

yi

Here, we adopt test image MRI of size 512x512 encoded by 8 bits per pixel, and with quadtree quantization T=10, the experimental of this results are compared with other value of quadtree quantization T=30. The experimental results are shown in table 1.

Sigma

 xi  xm 2   yi  ym 2

Where

(d)

Figure 6. Popular test images (a) MRI, (b) CT, (c) ECHO, (d) TOREX

 xm  yi  y m 

i

i

(c)

is the

is the mean intensity

 1 if the r  0 two images are absolutely identical, if they are r   1 completely uncorrelated, and if they are The correlation coefficient has the value r

T=30

r

i

(b)

i 1

Where I and Iˆ are respectively the reference and Iˆ I degraded images, i and i are the contents of images at the i-th local window. M : the total number of local windows in image. The MSSIM values exhibit greater consistency with the visual quality.

 x

(a)

completely anti-correlated. [14]. Copyright © 2014 MECS

I.J. Image, Graphics and Signal Processing, 2014, 3, 43-50

A Comparative Study between X_Lets Family for Image Denoising

8. (c), and it also marks that the PSNR decreases and this can be explained by increasing of sigma value which represents the noise variation that any role that degrade the quality visual of image. After showed the effectiveness of our algorithm for T = 30, this value is fixed in the following work. We have extended this study to a set of medical images, to demonstrate the effectiveness of bandelet transform, we vary the noise variance (sigma) and calculating the evaluation parameters (PSNR, MSSIM); we obtain the following results (Table 2):

32 T=10 T=30

30 28 26 PSNR(dB)

47

24 22 20 18 16 0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

TABLE 2. NUMERICAL RESULTS OBTAINED AFTER CT, ECHO AND TOREX IMAGE DE-NOISING FOR T=30

Sigma

(a) PSNR Variation Image Sigma

0.9 T=10 T=30

0.85 0.8

MSSIM

0.65 0.6 0.55 0.5 0.45 0.05

0.1

0.15

0.2

0.25

0.3

0.35

ECHO

TOREX

PSN R(dB)

MSS IM

PSNR (dB)

MSSI M

PSNR (dB)

MSSI M

0.0 6

29.70 23

0.81 09

28.67 89

0.776 6

32.51 78

0.810 6

0.0 8

27.78 28

0.77 02

27.19 03

0.730 3

31.05 77

0.768 3

0.1

26.05 52

0.73 74

26.05 59

0.688 8

29.89 23

0.735 4

0.4

17.61 57

0.48 42

19.27 40

0.468 3

21.38 82

0.549 4

0.75 0.7

CT

0.4

Sigma

(b) MSSIM Variation Figure 7. Comparisons of MRI denoising image using bandelet transform between T=10 to T=30

34 MRI CT ECHO TOREX

32 30

PSNR(dB)

28 26 24 22 20

(a)

(b)

18 16 0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Sigma

Figure 9. Comparisons between MRI, CT, ECHO and TOREX denoising image using bandelet transform for T=30

(c) Figure 8. Denoising MRI images for different values of quadtree quantization T : (a) Noise image, (b) De-noising image for T=10, (c) De-noising image for T=30.

It can be seen from Table 1, that our algorithm presents excellent de-noising performance for T=30, Fig Copyright © 2014 MECS

(a)

(b)

I.J. Image, Graphics and Signal Processing, 2014, 3, 43-50

48

A Comparative Study between X_Lets Family for Image Denoising

(c)

(d)

(e) Figure 11. (a) Noise TOREX image, (b) Denoising TOREX image using wavelet transform, (c) Denoising TOREX image using ridgelet transform, (d) Denoising TOREX image using curvelet transform, (e) Denoising TOREX image using contourlet transform. 34 WAVELET RIDGELET CURVELET CONTOURLET BANDELET

32 30

(e)

(f) PSNR(dB)

28

Figure 10. Denoising CT, ECHO and TOREX images for T=30: (a) Noise CT image, (b) Denoising CT image, (c) Noise ECHO image, (d) Denoising ECHO image, (e) Noise TOREX image, (f) Denoising TOREX image

26 24 22 20

After comparing between the four curves In Fig 9. We can see that the bandelet transform is very effective and adaptable to TOREX image compared to MRI, CT images and ECHO this is justified by the values of PSNR. In the following, we make a comparative study of filtering between bandelet, contourlet, curvelet, ridgelet transforms and wavelet in TOREX medical image. The results obtained are as follows:

18 0.05

0.1

0.15

0.2 0.25 Rc(bpp)

0.3

0.35

0.4

Figure 12. Comparisons between bandelet, contourlet, curvelet, ridgelet and wavelet transform for TOREX image

From Fig 12, we clearly perceive the importance of the bandelet transform compared with wavelet, ridgelet, curvelet transform and contourlet; this is proven with the PSNR values. Fig 13 shown correlation coefficients results for a five transforms types used in de-noising domain to detect changes in an image. 1

(a)

(b)

CORRELATION COEFFICIENT

0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.05

(c)

Copyright © 2014 MECS

(d)

WAVELET RIDGELET CURVELET CONTOURLET BANDELET

0.1

0.15

0.2 0.25 SIGMA

0.3

0.35

0.4

Figure. 13 Comparisons between correlation coefficient for a five wavelet transforms

I.J. Image, Graphics and Signal Processing, 2014, 3, 43-50

A Comparative Study between X_Lets Family for Image Denoising

From the figure above we can say that the correlation coefficient from bandelet transform gives better results compared to other types of transforms. After showing the performance of the de-noising medical images, we apply our algorithm to the denoising satellite images. We are interested in this application by the satellite image gray scale coded on 8 bpp of size 512x512.

Figure 14. SATELLITE image

49

VI. CONCLUSION In this paper, we presented a new de-noising algorithm using a new transform used in processing image, which is called bandelets transform. The proposed method was applied for comparison between two type image (medical and satellite) of size 512X512X8 pixels contaminated by random noise. The comparison between different image using bandelet transform allows us to check the superiority of the bandelet transform in medical image hich’s stified by the PSNR and MSSIM highest values. Moreover, the bandelet transform provides compact representation and a major improvement compared to other classical transforms. We can assure that the bandelet transform outperforms the wavelet, the ridgelet, and the curvelet transform in term of PSNR values and visual quality which is the most pleasant among the all. The performance of the de-noising algorithm using the bandelet transform also performs well even in the cases where we have images with very high frequencies. In the future we are going to work into defining a strategy to exploit the bandelet transform for image compression.

34 SATELLITE THOREX

32

REFERENCES

30

PSNR(dB)

28 26 24 22 20 18 0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Sigma

Figure 15. Comparisons between TOREX and SATELLITE denoising image using bandelet transform for T=30

(a)

(b)

Figure. 16 Denoising SATELLITE for T=30: (a) Noise SATELLITE image, (b) De-noising SATELLITE image.

From Fig 15, we see that the gain between satellite image and medical is very important, which shows the effectiveness of the de-noising image using bandelet transform for medical image (TOREX).

Copyright © 2014 MECS

[1] E.J.Candes and D. L.Donoho, "Ridgelets: A key to higherdimensional intermittency", Philosophical Trans of the Royal Society of London Series A, vol.357, pp.2495-2509, 1999. [2] Minh N. Do and Martin Vetterli, "Image Demising using Orthonormal Finite Ridgelet Transform PTOCS. PIE, Wavelet Applications in Signal and Image Processing VIII", Akrain hldroubi; Andrew F. Laine; Michael A. Unser; Eds. Vol. 41 19, p. 831-842, Dec. 2000. [3] E. Le Pennec et S. Mallat, "Représentation d’images par bandelettes et application la compression", Dans GRETSI, Toulouse, Septembre 2001. [4] E. Le Pennec, "Bandelettes et représentation géométrique des images", Thèse de Doctorat, Ecole Polytechnique, 19 décembre 2002. [5] V. Chappelier, "Codage progressif d'images par ondelettes orientées", Thèse de Doctorat, UniversitéRennes 1, 15 décembre 2005. [6] Jian-Jiun Ding, "Time Frequency Analysis Tutorial", R99942057. [7] iaokai Wang, ingh ai ao, “Image enoising Method Based on Nonsubsampled Contourlet Transform and Bandelet Transform, The st International Conference on Information Science and Engineering (ICISE), Institute of Wave and Information, i’an iaotong niversity, i’an, China, 2009. [8] Hong Han,Xing Wu, "Research of Method in Human Detection Based on Bandelet Transform", Laboratory of Intelligent Perception and Image

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Mohammed BELADGHAM was born in Tlemcen, Algeria; he's received the electrical engineering diploma from university of Tlemcen, Algeria, and then a Magister in signals and systems from university of Tlemcen, Algeria and the Ph.D. degree in Electronics from the University of Tlemcen (Algeria), in 2012. His research interests are Image processing, Medical image compression, wavelets transform and optimal encoder. Yassine HABCHI was born in Mechria, Algeria, received his Bachelor (2005) and Engineers (2010) degree in Electrical Engineering from Saï da University in Algeria, and his Magister (2013) degree in Electronic from university of Bechar, Algeria. His current research interest includes Image processing, Medical image compression, wavelets transform and optimal encoder.

day I work in the Bechar University as lecturer. Since May 2009, I graduated PhD Es Sciences at the of Sidi Bel Abbes. I do my research at the Bechar University and Communications, Architecture and Media Laboratory (CAMR) (Djillali LIABES University). His research interests are Image transmission, Image processing, and digital transmission performances. Abdesselam Bassou was born in Bechar, Algeria. He received the Dipl.El.-Ing. Degree from the University of Tlemcen, Algeria in 1997, his Master from the University of Sidi Bel Abbes, Algeria in 2000, and his Doctoral degree Es Abdesselam Bassou was born in Bechar, Algeria. He received the Dipl.El.-Ing. Degree from the University of Tlemcen, Algeria in 1997, his Master from the University of Sidi Bel Abbes, Algeria in 2000, and his Doctoral degree Es Science from the University of Sidi Bel Abbes, Algeria in 2006. Actually, He is an Associate Professor at University of Bechar, Algeria. His main interests are digital signal processing, turbo encoding schemes and iterative decoding over fading channels, and channel equalization. AbdelmalikTALEB-AHMED Was born in Roubaix, France, in 1962. He received a post graduate degree and a Ph. D. in Electronics and Microwaves from the University of Lille1 in 1988 and 1992. From 1992 to 2004, He was an Associate Professor at the University of Littoral, Calais. Since 2004, He is currently a Professor at the University of Valenciennes in the department GE2I, and does his research at the LAMIH FRE CNRS 3304 UVHC, His research interests includes signal and image processing. Image segmentation, Prior knowledge integration in image analysis, Partial Differential Equations and Variational Methods in image analysis, Image compression, Multimodal signal processing, Medical image analysis, including multimodal image registration, etc..

MOULAY LAKHDAR I got my Engineering Degree in Telecommunication in 2000 at the Institute of Telecommunications in Oran. Magister was my second degree in Signal and telecom at Djillali LIABES university of Sidi Bel Abbes in 2003. From 2004 to this Copyright © 2014 MECS

I.J. Image, Graphics and Signal Processing, 2014, 3, 43-50