Three-dimensional speckle reduction in optical coherence ... - cpvrLab

Three-dimensional speckle reduction in optical coherence tomography through structural guided filtering Cyrill Gyger Roger Cattin Pascal W. Hasler Peter Maloca

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Optical Engineering 53(7), 073105 (July 2014)

Three-dimensional speckle reduction in optical coherence tomography through structural guided filtering Cyrill Gyger,a,b Roger Cattin,b Pascal W. Hasler,a,* and Peter Malocaa a

University Hospital Basel, Department of Ophthalmology, Mittlere Strasse 91, 4031 Basel, Switzerland Bern University of Applied Sciences, Institute for Human Centered Engineering, Computer Perception and Virtual Reality Lab, Quellgasse 21, 2502 Biel/Bienne, Switzerland b

Abstract. Optical coherence tomography (OCT) is a high-resolution noninvasive technology used in medical imaging for the spatial visualization of biological tissue. Due to its coherent nature, OCT suffers from speckle noise, which significantly degrades the information content of resulting scans. We introduce a new filtering method for three-dimensional OCT images, inspired by film grain removal techniques. By matching structural relatedness along all dimensions, the algorithm builds up vector paths for every voxel in the image volume representing its structural neighborhood. Then, by considering the information redundancy along these paths, our filter is able to reduce speckle noise significantly while simultaneously preserving structural information. This filter exceeds some common three-dimensional denoising algorithms used for OCT images, both in visual rendering quality and in measurable noise reduction. The noise-reduced results allow for improvement in subsequent processing steps, such as image segmentation. © 2014 Society of Photo-Optical Instrumentation Engineers (SPIE) [DOI: 10.1117/1.OE.53.7.073105]

Keywords: optical coherence tomography; speckle; three-dimensional image processing; noise in imaging systems; image recognition; algorithms and filters; medical and biological imaging. Paper 131751 received Nov. 25, 2013; revised manuscript received Apr. 14, 2014; accepted for publication Jun. 3, 2014; published online Jul. 23, 2014.

1 Introduction Optical coherence tomography (OCT) has become a widely established method of medical investigation over the past few years, particularly in the field of ophthalmological imaging.1,2 Today, OCT allows high-resolution three-dimensional (3-D) images of the posterior pole of the eye background, offering strong support for medical analyses and findings.3,4 However, the characteristic speckle noise present in OCT scans massively degrades OCT image quality, and, consequently, information content.5 Speckle noise is a result of the coherent scanning technique used in OCT, and it is generally present in all coherent image acquisition techniques, such as ultrasonic and synthetic aperture radar (SAR). In OCT, the coherent light gets reflected and scattered in the tissue, so that one part of the incident light undergoes multiple scattering. The coherent part of the backscattered wave front contains both a useful signal part and an “unwanted” signal part, a situation which is caused by multiple forward scattering and multiple backscattering from closely separated refractive index heterogeneities.5 This phenomenon, known as coherent backscattering, allows coherent interference of the useful and the unwanted signal parts. This distorts the intensity value for the scanned point, and thus leads to an error in the corresponding pixel value (brightness) of the digitized scan image. Many attempts have been made to reduce this noise, either directly within the scanning process6–11 or by postprocessing the obtained image data.12–34 Hybrid methods, which consider both the acquisition and algorithmic postprocessing, have also been introduced.35–38 Improvements in the acquisition process usually involve significant changes to the design of OCT systems that will allow researchers to acquire

several scans with uncorrelated speckle patterns. Such scans can be obtained through the compounding of space, frequency, or time or through polarization diversity.39 These hardware speckle reduction techniques are initially promising. However, it is a challenge to acquire a series of images that have, at the same time, as small as possible changes in the image structures and obviously different speckle patterns; this involves much more complex OCT systems and often leads to longer acquisition times. Nowadays, the acquisition time is practicable for averaging single slices (B scan) through a relatively small number of corresponding scans (e.g., devices from Heidelberg Engineering and Bioptigen Inc., support image registration and averaging of single slices). However, these averaged results usually still contain speckle patterns and grainy structures, due to the still-limited number of images included for averaging and limitations in the registration process. For 3-D OCT (multislice or C scan), the challenge is even greater. Only some experimental research devices allow for the instantaneous recapturing of an entire image volume in a short enough period that it can be used for averaging. Thus, the design of algorithmic postprocessing steps remains important. Such methods consider the resulting image data in calculating image improvements offline, and can utilize several times as much calculation power as that which was used during the acquisition process. A broad range of noise reduction algorithms have been built for or adapted to speckle noise and/or OCT, both for two-dimensional (2-D) images12–31,33,34 and for (3-D) image stacks.29,32 Such methods include averaging with fixed kernels,12 stick-based rotating kernels,13,14 and nonlocal kernels,15 median and variational approaches,16 adaptive

*Address all correspondence to: Pascal W. Hasler, Email: [email protected]

0091-3286/2014/$25.00 © 2014 SPIE

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Gyger et al.: Three-dimensional speckle reduction in optical coherence tomography. . .

filtering like that used by Lee and Frost,17–20 anisotropic diffusion21–24 and total variation denoising,25,26 Wiener filter,27 wavelet transformations,28–30 curvelet transformations,31,32 and the estimation of the noise-free data using Bayesian estimators.33,34 Some of these approaches have led to significant findings and improvements, but most still suffer from the drawback of either blurred structural information or insufficient speckle reduction capability. In this paper, a 3-D noise reduction method inspired by film grain removal filters is introduced. This method exceeds some common 3D denoising algorithms used for OCT images both in visual rendering quality and in measurable noise reduction. In terms of noise reduction and structure preservation in the context of 3-D OCT, it provides remarkably good performance. This paper is structured as follows. First, we briefly reconsider the characteristics of speckle noise. Next, we introduce our method, outline the basic idea behind our filter, and present its architecture. After that we describe our testing environment. The speckle noise simulation used to measure and evaluate the filter results is explained, and the metrics used in our tests are shown. We present our results and compare our filter’s performance with those of established speckle reduction filters used in OCT imaging. In addition, we show a preliminary application in an image segmentation that is clearly improved by our filter. We discuss the results and fields of use for our filter, and then offer a conclusion regarding our findings. 2 Speckle Characteristics Speckle noise is a random deterministic effect.40 Multiple scattering manipulates a single wave randomly in both its phase and its amplitude. The signal components of a wave are thereby influenced by every single scatterer. Theoretically, every scatterer can be seen as a phasor in the complex plane, and the resulting signal as a vector sum of such phasors. Such a phasor depends on the refractive index and on the physical size of the scatterer. Due to the vast number of scatterers in a given tissue that influence any single wave, the resulting signal can be seen as the outcome of a 2-D random walk in the complex plane with independently and identically normal distributed real and imaginary components with zero mean and identical standard deviation.41 The phasors, therefore, fit a circular normal distribution, also known as von Mises distribution, and the vector magnitudes of the phasors of such a multiple scattering process follow a Rayleigh distribution. Equation (1) shows the

probability density function of the Rayleigh distribution, where x is the stochastic variable and σ > 0 is the scale parameter of the distribution. fðx; σÞ ¼

x −x2 ∕2σ2 e ; σ2

x ≥ 0:

(1)

Hence, the noise-generated weighting part of the intensity values of a discretized OCT scan is Rayleigh-distributed. Figure 1 illustrates this fact, showing the histograms of two uniform areas in an OCT scan. The Rayleigh distribution pattern can be clearly observed in the pixel values. It can be seen that the spread of the Rayleigh distribution depends on the reflectivity of the tissue area. The more reflective a specific tissue part is, the more coherent backscattering occurs and the more the amplitude is manipulated by interference. Thus, this characteristic affects the multiplicative behavior of speckle noise in OCT. The fact that the noise intensity of a single discretized pixel varies randomly but follows a statistically distribution (Rayleigh) means that we can use redundancy to recognize and filter out the unwanted noise part. This mechanism is already widely used for B scan OCT, i.e., 2-D image scans. The scanning engine in recently developed devices allows for the successive capture of a series of single B scans at the same position, so that a representative value for each pixel can be determined by averaging the measurements of redundant positions. To ignore eye motions while capturing the series, the acquisition time is usually fast enough for this not to influence the successive scanning; alternatively, some kind of live motion compensation (usually active eye tracking) is used to ensure that the same position is scanned continually. Even though these mechanisms apparently enhance the visual quality of an OCT scan, speckle noise is still present in these images, and it is still interfering. Furthermore, in C scan OCT (3-D), the use of such live averaging methods is highly restricted, due to the long acquisition time and the greater amount of data required. 3 Method Our method considers redundancy as well, and, at the same time, uses the greater information content provided by 3-D scans, instead of single slice images. Redundancy is not only to be found at the exact same physical place; it also appears in related structures and objects in space. Our filter

Fig. 1 (a) OCT B scan image of anterior pig eye segment with red-marked regions of two uniform areas in the anterior chamber (I) and the cornea (II); (b) histograms of the red-marked regions in (a) clearly show the Rayleigh distribution of the present speckle noise.

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is inspired by film grain removal algorithms that take the temporal dimension of a film into account as a third dimension to filter out film grain. The AviSynth filter Temporal Degrain, for example, matches every pixel of a single film frame with the corresponding pixels in the n preceding and n succeeding frames (where 1 ≤ n ≤ 3). A simple block-matching algorithm is used to detect the movement of a single pixel between subsequent frames. In this way, a path consisting of related vectors in the temporal dimension is built up, representing the movement of a single point over several frames. All pixels along that path are collected and median filtered to approximate a representative value for the specific pixel. Thus, the information redundancy distributed over several frames is considered. Figure 2 illustrates how this filter mechanism functions. With the method described, theoretically, two vector paths of individual voxels from the same frame could pass through each other. Although additional checks during processing may avoid this, we did not examine this, since the robust block matching leads to a negligible amount of such crossovers.

The visual results of such a method are quite good, since film grain is randomly distributed, and the probability of grain existing at one and the same position in two successive frames is relatively low. The most important element in terms of quality is the block-matching method. Median filtering over pixels that do not correspond results in blurring and disruptive artifacts. Now, with our filter for 3-D OCT data, the idea of filtering related pixels along a specific dimension has been adapted and enhanced. Instead of having two spatial dimensions plus time, as it is the case for films, 3-D OCT has three spatial dimensions. Moreover, instead of matching motion, we match structural relatedness. However, the method for detecting this relatedness remains the same as that generally used for detecting motion (i.e., structural similarities). To increase the information content of all three dimensions, we do not filter only in one single dimension, but in all three dimensions. To adequately consider the different information densities (physical resolutions) of the 3-Ds, the filtering is done sequentially for each dimension in order to

Fig. 2 (a) Displacement and movement of some pixels in a film sequence, with the visualized motion vector of the highlighted (red-bordered) pixel among three frames; (b) frame n þ 1, containing some grain pixels; (c) frame n+1, with median filtered pixels along their individual motion vectors, containing no more grain.

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improve information density. In other words, the dimension with the largest physical distance between two pixels is considered first, the one with the second-largest physical distance second, and the one with the smallest distance last. This order ensures that the real image information present in the 3-D OCT scan will be utilized as much as (and as long as) possible. In the following, the determined relation vector path of a particular dimension D for a specific voxel I x at position x : ¼ ½x; y; z in the OCT volume I is viewed as the spatial neighborhood η¯ D x of that voxel, where this neighborhood is subclassified as a positive or negative neighborhood, depending on whether it runs in the positive or negative þ − ¯D direction of the considered dimension ð¯ηD x ;η x Þ. If I represents the original image volume and I x the value of a voxel at position x in that volume, the following equations describe our filter þ

−

þ

−

I Zx ¼ medðI n0 : : : njnj Þjn :¼ fx; η¯ Zx ; η¯ Zx g I Yx ¼ medðI Zn0 : : : njnj Þjn :¼ fx; η¯ Yx ; η¯ Yx g Xþ

þ

−

¯D ð¯ηD x ;η x Þ for every single voxel (x) in the volume, we avoid resolution loss while filtering. In Eq. (2), it is assumed that the physical information density of each dimension increases from Z to Y to X. Figure 3 illustrates the process of our filtering for one specific voxel. The size of the neighborhood, i.e., the number of vectors considered in the path of one particular voxel, is parameterizable. As shown later, in Sec. 5, we used values between 2 and 6 (per direction, resulting in 5 to 13 values for the whole path) for optimal results in our OCT volumes. The neighborhood determination is realized through a block-matching algorithm. As mentioned above, the performance of this algorithm, i.e., its matching criterion, is of great importance, since it is decisive in the quality of the filter results. We propose the integral projection as a block-matching criterion, given its noise robustness and strong contour consideration m X n n X X IP ¼ A½x; y − B½x; y x¼1 y¼1

X−

I^ x ¼ I Xx ¼ medðI Yn0 : : : njnj Þjn :¼ fx; η¯ x ; η¯ x g;

(2)

where medðÞ denotes the median, and n holds the spatial voxel coordinates (positions) of the values included for the median. Thus, the negative and positive neighborhoods, as well as the value at point x, are considered for the median each time. By using completely individual neighborhoods

y¼1

n X m m X X þ A½x; y − B½x; y: y¼1 x¼1

(3)

x¼1

In Eq. (3), A and B represent the two blocks that are to be compared with each other. A small IP value indicates a close match between the compared blocks; therefore, the smallest value indicates the most similarity.

Fig. 3 Illustration of the proposed filter mechanism: every voxel is filtered by collecting its corresponding neighboring voxels along its structural vector path in the specific dimension, and the values are median filtered. This step is repeated for all dimensions successively, in the order of their physical information density.

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We identified block sizes between 7 × 7 and 15 × 15 pixels, and carried out an exhaustive search for the best results with our image volumes (x∶512 pixels, y∶512 pixels, z∶576 pixels, Δx ¼ Δy ≅ 20 μm∕px, Δz ≅ 2.46 μm∕px). The recommended search area size for block matching depends heavily on the structural movement between the two considered frames, and therefore on physical resolution or intraslice distance. We used offset values between 11 and 22 pixels for intraslice distances for OCT scans of 11 microns or less. The exhaustive processing of every single voxel has significantly high computational costs. However, several optimization techniques can reduce these costs drastically. First, the vector paths of a considered dimension can be precalculated for the entire volume. This way, when collecting the voxels along each voxel’s neighborhood, the corresponding forward and backward vectors can just be looked up, eliminating repetitive calculation. Second, for the integral projection block matching, summed area tables can be used. Besides such implementation optimizations, the use of an appropriate parallel processing hardware can speed up calculations significantly. In our environment, we began with a computational time of about 1 h for a 512 × 512 × 512 voxel volume, and we ended up with a time of less than 10 s using a midrange commercial GPU and some of the implementation optimizations described above. All of these proposed optimizations do not change the calculation results anyhow, and therefore lead to equal quality but low-computational costs. 4 Testing To carry out any significant test of the noise reduction performance of our algorithm when compared with others, an adequate setup is needed. Denoise performance is often evaluated by considering the original noise-free image and the denoised one, which itself is the denoising result of a noise-added version of the original. Unfortunately, there is no way to obtain an original, noise-free version of an OCT image (indeed, if there were, our efforts would be worthless) and, as mentioned in the introduction, noisereduced scans obtained by averaging several scans from the same physical position are not available for C scan OCT (3-D). Given the absence of such a “gold standard” for 3-D OCT, we needed to simulate speckle noise and add it artificially to a given image. With this setup, all common noise measurement methods can be used easily, taking both the noise-free original and the denoised result into account. 4.1 Speckle Noise Simulation As explained in Sec. 2, speckle noise is a Rayleigh-distributed multiplicative noise. The simulation of speckle noise can therefore be realized by implementing this statistical model. Another way to simulate speckle noise is by implementing the whole random walk process for every pixel. We decided to use the first method, due to its better time performance. The pixel value of a speckle-influenced resolution cell can be represented by a multiplicative model with exponential distribution. Let IðxÞ be the resulting pixel value of the pixel coordinates x :¼ ½x; y. RðxÞ represents the reflectivity at point x and uðxÞ represents the multiplicative speckle Optical Engineering

noise. Thus, uðxÞ is statistically independent of RðxÞ; it represents the results of the random walk and is Rayleighdistributed. IðxÞ ¼ RðxÞuðxÞ:

(4)

The interference of the backscattering process can influence the amplitude constructively or destructively. The variation in the origin pixel value caused by speckle noise can therefore be negative or positive. The mean intensity value of the distorted pixels, therefore, should correlate with the intensity value of the original image. This ensures that an equivalent number of destructive and constructive interferences is represented. In terms of Eq. (4), this means that uðxÞ should have a mean value of 1, independent of the standard deviation σ used. Because the mean of the Rayleigh distribution depends on the standard deviation, a mean correction is needed here. We apply this requirement by transforming Eq. (4) to rffiffiffi π I 2 ðxÞ ¼ RðxÞ − σ RðxÞ þ kðσÞRðxÞ: (5) 2 The random component uðxÞ of Eq. (4) is thereby replaced by kðσÞ, which represents a simple Rayleigh distribution pffiffiffiffiffiffiffiffiwith a standard deviation of σ. The subtraction of σ pffiffiffiffiffiffiffiffi π∕2RðxÞ represents the mean correction, where σ π∕2 is the mean of an arbitrary Rayleigh distribution with a standard deviation of σ. The noise is built by the random component kðσÞ, and the reflectivity RðxÞ is added to the original value, from which the mean correction has been already subtracted. In this way, the mean of the Rayleigh-distributed noise is always equal to the local reflectivity. The factor uðxÞ of Eq. (4) can still be reconstructed uðxÞ ¼ I 2 ðxÞ∕RðxÞ;

(6)

where uðxÞ is still a statistically independent Rayleighdistributed factor and thus still fulfills the conditions for Eq. (4). Figure 4 shows an example of our simulated speckle noise. The histogram clearly shows the Rayleigh distribution and its multiplicative behavior.

4.2 Measurement For representative results, the use of a synthetic image with characteristics similar to those in OCT is important. We constructed an image stack with key aspects, such as blood vessels, the choroid, and depth-dependent decreasing global reflectivity similar to a retinal C scan OCT (see Fig. 5). The blood vessels vary in depth, are tortuous, and translate within the frames. These vessel properties are illustrated in Fig. 5(c), which shows a 3-D rendering of the vessels underneath the choroid. We then added synthetic speckle noise to the volume based on the algorithm proposed in Sec. 4.1 [see Fig. 5(b)]. To determine noise reduction capability, we use the peak signal-to-noise ratio (PSNR), the root-mean-square error (RMSE), and the structural similarity (SSIM). The SSIM is able to assess the denoising performance not only through the cumulative differences or variations, but also by considering structural differences a filter has caused in the filtered

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Fig. 4 (a) Simulated speckle noise in synthetic image; (b) the corresponding histogram clearly shows the Rayleigh distribution and its multiplicative behavior [the grayscale denotes the corresponding regions in (a)].

image. We, thus, avoid misleading results based on simple metrics, and the results are much more reliable.42 We compare the results of our method with four widely established filter techniques used in speckle reduction: the Lee filter,17 the Frost filter,19 anisotropic diffusion,21 and total variation denoising.25 For a fair and more representative comparison with our own filter, we use 3-D neighborhoods for all filters considered, thereby extending them to 3-D filters. To evaluate our results with the synthetic test data, we also compare it to slice averaging and slice median filtering. As mentioned in the introduction, slice averaging can be found in many recent OCT devices. It is often combined with a preceding registration procedure, and is commonly used to

produce “gold-standard” high-SNR images. However, since averaging only exists for single slices, we cannot consider slice averaging and slice median filtering for our real clinical data, which are exclusively 3-D OCT volumes. In their original design, both adaptive filters (Frost and Lee) suppose normally distributed noise. However, as described in Sec. 2, speckle noise in OCT follows a Rayleigh distribution. Now, we adapt the statistical properties in the Frost and Lee filters to a Rayleigh distribution, resulting in a different variance varðXÞ ¼

4−π 2 σ ≈ 0.429σ 2 : 2

(7)

Fig. 5 Test sample volume: (a) one single slice of synthetic image volume of a retinal C scan OCT containing some blood vessels, the choroid, and depth-dependent decreasing global reflectivity; (b) the same scan with simulated speckle noise; (c) 3-D rendering of the vessels underneath the choroid.

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Table 1 Quantitative results and comparison.

PSNR

RMSE

SSIM

Slice averaging

38.591

2.846

0.949255

Slice median filtering

38.041

3.032

0.926918

Total variation

31.314

6.578

0.966546

Lee filter

34.622

4.495

0.979956

Frost filter

36.286

3.711

0.988084

Anisotropic diffusion

33.677

5.012

0.973138

Proposed

41.242

2.099

0.992382

Our results show that, for both filters, this adaption leads to a better visual performance in OCT speckle noise. Therefore, we consider these adapted versions in the comparison with our filter. 5 Results We have determined the best parameterization for each filter method and applied them to our artificially noisy test image volume. For slice averaging and slice median filtering, 10

samples of the same slice with individual noise are considered. The subsequent measurements all consider the noisefree original of the test image volume. The quantitative results show that our filter clearly exceeds all of the comparison filters in all quantitative measurement criteria (see Table 1). Our method not only overtops the other filters in the classical noise assessment indicators PSNR and RMSE, but also in the SSIM measurement, which emphasizes its strong preservation of structural information. These results are further confirmed by comparing the visual outcome of our filter with the other methods we considered. As Fig. 6 shows, total variation denoising, Lee, Frost, and anisotropic diffusion all lead either to strong smoothing or to fraying of edges and contours. The Frost filter is able to homogenize the uniform tissue area fairly well, but it still fails in filtering hard contours. Both slice averaging and slice median filtering show good results in terms of structural retention, but they fail to cleanly homogenize individual segment areas. Our filter not only removes the noise in all areas almost completely, but it also manages to avoid smoothing out or fraying of the blood vessel edges. The filter result is almost indistinguishable from the original sample. Figure 7 shows the results of all considered filters with a real OCT image stack. As mentioned, slice averaging and slice median filtering cannot be considered for comparison here, due to the physical restrictions in capturing C scan

Fig. 6 Visual comparison I (showing a slice of respective image volume): (a) original synthetic sample; (b) same, with speckle noise added. Results of respective filtering: (c) slice averaging; (d) slice median filtering; (e) total variation denoising; (f) Lee; (g) Frost; (h) anisotropic diffusion; and (i) proposed filter.

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Fig. 7 Visual comparison II (showing a slice of respective image volume): (a) original OCT sample. Results of respective filtering: (b) total variation denoising; (c) Lee; (d) Frost; (e) anisotropic diffusion; and (f) proposed filter. Image volume sample data courtesy of Medical University of Vienna.

Fig. 8 Profile plot comparison: (a) one slice of the synthetic test volume with highlighted profile line. Profile plots of respective filtering results (blue represents the original profile, red the filtered one); (b) slice averaging; (c) slice median filtering; (d) total variation denoising; (e) Lee; (f) Frost; (g) anisotropic diffusion; and (h) proposed filter.

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Fig. 10 3-D rendering of anterior pig eye volume showing a side-byside comparison of unfiltered and filtered image volumes.

Fig. 9 (a) One unfiltered slice of anterior pig eye volume; (b) the same slice after filtering the image volume with our proposed filter method.

OCT images. We even desist from approximated averaging, which would involve the consideration of the neighboring slices directly succeeding and directly preceding a real OCT volume. This would only lead to a strong blurring of the image structures. The real data comparison also highlights the performance of our method. Total variation denoising, Frost, Lee, and anisotropic diffusion all suffer from insufficient preservation of important contours and are still distorted by strong noise artifacts, whereas our method shows clear and even enhanced contours and is able to homogenize related tissue layers. Illustrating our filter’s excellent performance in terms of edge preservation and noise reduction, Fig. 8 compares the profile plots of all considered filters and our proposal. Even when compared to slice averaging and slice median filtering, our method clearly shows a more homogeneous curve, indicating better noise reduction in regions that are actually homogeneous. Finally, Fig. 9 shows an impressive demonstration of the noise reduction capability of our proposed method. The structures of the filtered OCT scan of the anterior pig eye segment are detailed, and the contours are sharp. Important contours are enhanced, while no image details are lost. The image filtered with our proposed method can be classified as almost noise-free. In addition, Fig. 10 shows a 3-D rendering of the whole pig eye volume showing the noise reduction capability of the proposed filter side by side. Preliminary tests also show that OCT volumes filtered by the proposed method improve any subsequent automatic segmentation. Figure 11 shows the results of a global 3-D twolabel level set segmentation on (1) the unfiltered original image volume and on (2) the denoised image volume, filtered by our method. The segmentation was parameterized to locate the choroidal blood vessels in the retinal OCT volume. The segmentation on the unfiltered image is misguided by the speckle noise, delivering an almost unusable result. The result of the segmentation on the image filtered by our method is clearly more precise, as it represents the Optical Engineering

Fig. 11 Filter influence to segmentation: showing one slice of respective segmentation result of retinal volume scan: (a) unfiltered original image volume; (b) image volume filtered with the proposed method before segmentation.

blood vessel contours much more faithfully. As the contours of the retinal layers are also enhanced by the proposed filter, layer segmentation could be facilitated as well. 6 Conclusion Our proposed filter method is able to greatly improve speckle noise-disturbed OCT image stacks in terms of visual quality and quantitative measurements. Noise can be drastically reduced visually, and the smoothing or fraying of edges and contours is also prevented. In fact, by considering structural relatedness while filtering, contours and edges are enhanced. Compared to some widely established filters for speckle noise reduction (Frost, Lee, total variation denoising, anisotropic diffusion), as well as to high-SNR images produced by slice averaging and slice median filtering, our filter exceeds all measured results of noise and structure preservation indicators (PSNR, RMSE, and SSIM). In ophthalmological OCT, the results of our method allow the ophthalmologist to analyze the scan more precisely, providing insights that are not visible in the unfiltered image. The denoised volumes also enhance the results of automatic segmentations, which open up new possibilities in retinal eye segmentation.

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Acknowledgments The authors gratefully acknowledge the HuCE optoLab of the Berne University of Applied Sciences, especially Christoph Meier and Christoph Höschele, for the provision of OCT image material. The authors’ appreciation also goes to the Centre for Medical Physics and Biomedical Engineering of the Medical University of Vienna, and especially to Boris Povazay, for providing sample materials. References 1. D. Huang et al., “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991). 2. J. G. Fujimoto et al., “Optical coherence tomography (OCT) in ophthalmology: introduction,” Opt. Express 17(5), 3978–3979 (2009). 3. M. Wojtkowski et al., “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Ophthalmology 112(10), 1734–1746 (2005). 4. W. Drexler and J. G. Fujimoto, “Three-dimensional retinal imaging with high-speed ultrahigh-resolution optical coherence tomography,” Prog. Retin. Eye. Res. 27(1), 45–88 (2008). 5. J. M. Schmitt, S. H. Xiang, and K. M. Yung, “Speckle in optical coherence tomography,” J. Biomed. Opt. 4(1), 95–105 (1999). 6. A. E. Desjardins et al., “Speckle reduction in OCT using massivelyparallel detection and frequency-domain ranging,” Opt. Express 14(11), 4736–4745 (2006). 7. J. M. Schmitt, “Array detection for speckle reduction in optical coherence microscopy,” Phys. Med. Biol. 42(7), 1427–1439 (1997). 8. H. W. Ren et al., “Phase-resolved functional optical coherence tomography: simultaneous imaging of in situ tissue structure, blood flow velocity, standard deviation, birefringence, and stokes vectors in human skin,” Opt. Lett. 27(19), 1702–1704 (2002). 9. M. Pircher et al., “Speckle reduction in optical coherence tomography by frequency compounding,” J. Biomed. Opt. 8(3), 565–569 (2003). 10. B. Karamata et al., “Spatially incoherent illumination as a mechanism for cross-talk suppression in wide-field optical coherence tomography,” Opt. Lett. 29(7), 736–738 (2004). 11. J. Kim et al., “Optical coherence tomography speckle reduction by a partially spatially coherent source,” J. Biomed. Opt. 10(6), 064034 (2005). 12. M. Pircher et al., “Measurement and imaging of water concentration in human cornea with differential absorption optical coherence tomography,” Opt. Express 11(18), 2190–2197 (2003). 13. J. Rogowska and M. E. Brezinski, “Evaluation of the adaptive speckle suppression filter for coronary optical coherence tomography imaging,” IEEE Trans. Med. Imaging 19(12), 1261–1266 (2000). 14. C. Y. Xiao, Z. Su, and Y. Z. Chen, “A diffusion stick method for speckle suppression in ultrasonic images,” Pattern Recogn. Lett. 25(16), 1867–1877 (2004). 15. A. Buades, B. Coll, and J. M. Morel, “A review of image denoising algorithms, with a new one,” Simulation 4(2), 490–530 (2005). 16. F. Zahedi and R. Thomas, “A maximum homogeneity based median filter,” in Proc. IEEE Colloquium on Morphological and Nonlinear Image Processing, pp. 7, IET, London (1993). 17. J. S. Lee, “Speckle analysis and smoothing of synthetic aperture radar images,” Graph. Model. Im. Proc. 17(1), 24–32 (1981). 18. M. Mansourpour, M. A. Rajabi, and J. A. R. Blais, “Effects and performance of speckle noise reduction filters on active radar and SAR images,” in Proc. ISPRS Ankara Workshop on Topographic Mapping from Space, Vol. XXXVI-1/W41, ISPRS, Turkey (2006). 19. V. S. Frost et al., “A model for radar images and its application to adaptive digital filtering of multiplicative noise,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-4(2), 157–166 (1982). 20. R. Vanithamani and G. Umamaheswari, “Performance analysis of filters for speckle reduction in medical ultrasound images,” Int. J. Comput. Appl. T. 12(6), 23–27 (2010). 21. P. Perona and J. Malik, “Scale-space and edge detection using anisotropic diffusion,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990). 22. Y. Yu and S. T. Acton, “Speckle reducing anisotropic diffusion,” IEEE T. Image Process. 11(11), 1260–1270 (2002). 23. P. Puvanathasan and K. Bizheva, “Interval type-II fuzzy anisotropic diffusion algorithm for speckle noise reduction in optical coherence tomography images,” Opt. Express 17(2), 733–746 (2009). 24. D. C. Fernández, H. M. Salinas, and C. A. Puliafito, “Automated detection of retinal layer structures on optical coherence tomography images,” Opt. Express 13(25), 10200–10216 (2005). 25. L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Physica D 60, 259–268 (1992).

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26. L. Wang et al., “Nonlocal total variation based speckle noise removal method for ultrasound image,” in Proc. 2011 Fourth Int. Congress on Image and Signal Processing (CISP), pp. 709–713, IEEE, Shanghai (2011). 27. A. Ozcan et al., “Speckle reduction in optical coherence tomography images using digital filtering,” J. Opt. Soc. Am. A 24(7), 1901–1910 (2007). 28. D. C. Adler, T. H. Ko, and J. G. Fujimoto, “Speckle reduction in optical coherence tomography images by use of a spatially adaptive wavelet filter,” Opt. Lett. 29(24), 2878–2880 (2004). 29. M. Gargesha et al., “Denoising and 4D visualization of OCT images,” Opt. Express 16(16), 12313–12333 (2008). 30. P. Puvanathasan and K. Bizheva, “Speckle noise reduction algorithm for optical coherence tomography based on interval type II fuzzy set,” Opt. Express 15(24), 15747–15758 (2007). 31. Z. P. Jian et al., “Speckle attenuation in optical coherence tomography by curvelet shrinkage,” Opt. Lett. 34(10), 1516–1518 (2009). 32. Z. P. Jian et al., “Three-dimensional speckle suppression in optical coherence tomography based on the curvelet transform,” Opt. Express 18(2), 1024–1032 (2010). 33. A. Wong et al., “General Bayesian estimation for speckle noise reduction in optical coherence tomography retinal imagery,” Opt. Express 18(8), 8338–8352 (2010). 34. A. Achim, A. Bezerianos, and P. Tsakalides, “Novel Bayesian multiscale method for speckle removal in medical ultrasound images,” IEEE Trans. Med. Imag. 20(8), 772–783 (2001). 35. F. Forsberg, S. Leeman, and J. A. Jensen, “Assessment of hybrid speckle reduction algorithms,” Phys. Med. Biol. 36, 1539 (1991). 36. A. W. Scott et al., “Imaging the infant retina with a hand-held spectraldomain optical coherence tomography device,” Am. J. Ophthalmol. 147(2), 364–373 (2009). 37. M. Szkulmowski et al., “Efficient reduction of speckle noise in optical coherence tomography,” Opt. Express 20(2), 1337–1359 (2012). 38. L. Fang et al., “Sparsity-based denoising of spectral domain optical coherence tomography images,” Biomed. Opt. Express 3(5), 927–942 (2012). 39. J. W. Goodman, “Some fundamental properties of speckle,” J. Opt. Soc. Am. 66(11), 1145–1150 (1976). 40. M. V. Sarode and P. R. Deshmukh, “Reduction of speckle noise and image enhancement of images using filtering technique,” Int. J. Adv. Technol. 2(1), 30–38 (2011). 41. E. Ng, “Speckle noise reduction via homomorphic elliptical threshold rotations in the complex wavelet domain,” MS Thesis, University of Waterloo (2005). 42. C. Perreault and M. F. Auclair-Fortier, “Speckle simulation based on b-mode echographic image acquisition model,” in Proc. Fourth Canadian Conf. on Computer and Robot Vision, pp. 379–386, Montreal, Quebec (2007). 43. Z. Wang et al., “Image quality assessment: from error visibility to structural similarity,” IEEE T. Image Process. 13(4), 600–612 (2004). Cyrill Gyger received his BSc in computer science from the University of Applied Sciences of Northwestern Switzerland and his MSc in engineering from the Bern University of Applied Sciences, where he subsequently served as a Research Associate at the cpvrLab. He is currently member of the OCT research laboratory at the University Eye Clinic Basel and is working for Xovis AG, Switzerland. His research focuses on digital image processing, especially on image segmentation and filtering. Roger Cattin is a professor emeritus for Computer Perception and Virtual Reality at the Bern University of Applied Sciences, Switzerland. Due to his vast experience in the field of digital signal and image processing he still is coaching the OCT research laboratory of the University Eye Clinic Basel, Switzerland. Pascal W. Hasler, MD, was a medical and vitreoretinal fellow at the Department of Ophthalmology, Glostrup, Denmark. He promoted to a senior consultant for medical and surgical retina at the University Eye Clinic Basel, Switzerland. His scientific focus is placed on vitreoretinal and macular eye diseases. Peter Maloca is a doctor of ophthalmology, especially surgery. Since years he has been a specialist in the development of software and hardware for Optical Coherence Tomography (OCT). In addition to his clinical occupation in his office, he currently is a research fellow at the OCT research laboratory of the University Eye Clinic Basel, Switzerland.

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Vol. 53(7)