A NON LOCAL APPROACH FOR SAR IMAGE

DENOISING

Sara Parrilli, Mariana Poderico, Cesario Vincenzo Angelino, Giuseppe Scarpa,

Luisa Verdoliva

To cite this version:

Sara Parrilli, Mariana Poderico, Cesario Vincenzo Angelino, Giuseppe Scarpa, Luisa Verdoliva.A NON LOCAL APPROACH FOR SAR IMAGE DENOISING. IEEE IGARSS, Jul 2010,Honolulu, Hawai, United States. 2010. <hal-00518135>

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A NONLOCAL APPROACH FOR SAR IMAGE DENOISING

S. Parrilli 1, M. Poderico 1, C.V. Angelino 1,2, G. Scarpa 1, L. Verdoliva 1

1 DIBET, University Federico II of Naples, Italy2 Laboratory I3S, University of Nice-Sophia Antipolis/CNRS, France

ABSTRACT

Speckle reduction is a key step in several SAR image pro-cessing procedures. In this paper, a new despeckling tech-nique based on the “nonlocal” denoising filter BM3D [1] ispresented. The filter has been modified in order to take intoaccount SAR image characteristics. The experimental results,conducted on both synthetic and real SAR images, confirmthe potential of the proposed approach.

Index Terms— Despeckling, Nonlocal Filtering, BM3D

1. INTRODUCTION

Because of the coherent nature of radar waves, and the sub-sequent coherent processing, SAR images are corrupted bya strong specific noise, called “speckle”. As a consequence,detecting objects and regions of interest in SAR images maybe a severe challenge even for an expert human interpreter,while automatic algorithms devoted to the same tasks are justnot reliable enough for most applications. For this reason, inrecent years there has been a growing interest on SAR im-age denoising, motivated also by the appearance of powerfultechniques based on wavelet transform.

Indeed, wavelet shrinkage techniques, like that originallyproposed by Donoho [2], have been readily applied to SARimages [3], with some good results. However, the waveletshrinkage approach relies on the hypotheses of additive andgaussian noise, while SAR speckle can be better modeled asmultiplicative noise. To circumvent this problem, a homo-morphic transformation is typically applied on the image be-forehand, so as to obtain additive noise. Then, the waveletcoefficients can be properly modeled in the log-domain andestimated by means of a bayesian approach, as proposed forexample in [4] and [5], before going back to the original do-main. This approach, relatively simple, has the drawback ofaltering the statistics of the original image, which might in-troduce unwanted artifacts. As an alternative, one can avoidthe log-transform altogether, and model instead the data as af-fected by a signal-dependent additive noise, using afterwardsa wavelet transform [6, 7, 8].

More recently, speckle reduction techniques based on the“nonlocal” approach have been gaining ground [9, 10, 11],building upon the nonlocal means algorithm originally pro-

posed in [12]. This approach relies on the observation thatmost images present clear self-similarities, as most patchesrepeat almost identically over and over in the image. Oncethese similar patches are identified, one can carry out someform of noise filtering along such patches, wherever they are,rather than in a local neighborhood of the pixel. A signifi-cant improvement w.r.t. the original algorithm, has been theevolution towards a multipoint rather than pointwise filter-ing, where the nonlocal approach is combined with waveletshrinkage in a two-step process. In the Block-matching 3D(BM3D) algorithm [1], once a group of similar patches iscollected, the whole group is denoised by means of a (3D)wavelet shrinkage process. Then the partially cleaned imageis used to estimate the parameters of a further denoising stepbased on Wiener filtering. It seems safe to say that BM3Drepresents the state of the art for images affected by whitegaussian noise.

In this work we propose a new version of BM3D which isadapted to denoise SAR images by taking into account theirpeculiar features. Experiments show the effectiveness of thenew technique both in terms of signal-to-noise ratio (on sim-ulated speckled images) and of subjective quality (on actualSAR images).

2. THE NONLOCAL APPROACH

Traditional denoising techniques, based on local filtering,make the implicit hypothesis that neighboring pixels have thesame statistical nature. Therefore, they work quite well onhomogeneous regions, significantly reducing noise power, buthappen to impair severely the image quality in the presenceof fine structures, details, and texture, which are typicallyoversmoothed. A plethora of adaptive techniques have beenproposed in time to deal with this problem but results remainrelatively poor.

The nonlocal approach [12] represents a complete changeof perspective since the “true” value of the current pixel isnot estimated anymore from the pixels that are closest to it,but from those pixels, located anywhere in the image, whichhave the most similar context. In more practical terms, foreach pixel, we consider the patch surrounding it, then lookin the whole image for the most similar patches (accordingto a weighted euclidean distance), and use the center pixels

of such patches to estimate the pixel value. Clearly, this ap-proach is particularly effective on quasi-periodic and texturedareas, where repeated patterns abound, but also in the pres-ence of edges and relatively small details.

Experimental results show nonlocal denoising techniquesto be very effective, at least for AWGN images. However,they can be easily adapted to work with different noise mod-els, such as the multiplicative one, provided that a suitablymodified distance measure is used. In the Probabilistic Patch-Based (PPB) algorithm [9], for example, a similarity criterionbased on the noise distribution model is considered, and thefiltering weights are obtained through an iterative processwhich takes into account the similarity between restoredpatches. Therefore, PPB works with both additive and mul-tiplicative noise, generalizing the original nonlocal-means(NL-means) algorithm.

NL-means itself, however, has been clearly surpassed bymore recent denoising techniques based on a nonlocal mul-tipoint approach, like the BM3D [1, 13], where both con-text and spatial correlation are taken into account to opti-mize results. The first action taken by BM3D, just like inNL-means, is to locate similar patches by means of a block-matching algorithm with Euclidean metric. Unlike in NL-means, however, all such patches are then collected in a 3Dstructure which undergoes a decorrelating transform (typi-cally wavelet) so as to exploit both spatial and contextual de-pendencies. Once a sparse representation is obtained, someforms of shrinkage is used to remove noise components (col-laborative filtering), before going back in the image domain.Since filtered patches can overlap, several estimates of thesame pixel are typically obtained, and their weighted aver-age must be computed to reconstruct a “basic estimate” of thedenoised image.

At this point, a further denoising step is carried out, whereblock-matching takes place on a cleaner image (the basic es-timate) so as to obtain more reliable matches, a new 3D struc-ture is created, and its empirical energy spectrum is com-puted to perform Wiener filtering on the transformed noisy3D structure.

3. MODIFIED BM3D FOR SAR IMAGE DENOISING

BM3D can be applied to SAR images as it is, provided thata homomorphic transform of the data is taken beforehand.As mentioned in the introduction, however, the log opera-tion changes the data dynamics and, therefore, the distancesamong patches. Based on such a consideration, we discardthe homomorphic approach, here, and work directly on theoriginal image. The first consequence of this choice is thatwe cannot use hard-thresholding anymore, since it does notmake any sense in this case, and must look for some othertype of wavelet shrinkage suitable for multiplicative noise.

As in classic BM3D, the first step is block matching. InBM3D an L2 distance is used to measure block similarity.

Indeed, if the noise variance is low, this kind of measure isrobust for independent additive noise, while if this is not thecase, a preliminary thresholding on the block wavelet coeffi-cients can be carried out to reduce noise power before com-puting block distances, as suggested in [1]. It is clear thatwe cannot use this strategy on speckled images, so we havechanged the measure for block distance as suggested in PPB.

After block-matching, our modified BM3D stacks simi-lar blocks together to form a 3D array, applies the undeci-mated wavelet transform, and finally performs shrinkage. Theshrinkage strategy used is very similar to that proposed by Ar-genti et al. in [6]. Let z be the observed noisy image and x thenoise-free reflectivity (we consider speckle intensity model),hence:

z(n) = x(n)u(n) = x(n) + [u(n)− 1]x(n)= x(n) + v(n),

(1)

where u(n) is the speckle that we suppose to be stationary,uncorrelated and independent of x(n). In addition, we as-sume that E[u(n)] = 1, that is E[u(n)− 1] = 0 which leadsus to consider an additive, zero-mean, signal-dependent noisemodel, represented in (1) by the term v(n).

In the transform domain (1) becomes

Wz(n) = Wx(n) + Wv(n), (2)

where Wy is the wavelet transform of a generic signal y. Asproposed in [6] we apply the following local linear MMSEestimator

Wx(n) = max(0,E[W 2

z (n)]− E[W 2v (n)]

E[W 2z (n)]

)Wz(n) (3)

to every detail subband of the UDWT decomposition (whichin our case is a 3D transform), and then carry out the inversetransform. For the hypotheses made on speckle noise, it ispossible to estimate E[W 2

v (n)] in the generic j-th subbandfrom the space-varying second-order moment of the noisy im-age z, as

E[W 2v (n)] =

σ2u

1 + σ2u

∑

i

heq(i)E[z2(n− i)] (4)

where heq is the equivalent filter of the j-th subband. Unlikein [6], where the statistics are computed pixel by pixel usinga 7× 7 local window, we reduce the computational burden byassuming E[z2(n)] to be constant in each 3D block, which isquite reasonable considering that they are usually quite small.This choice, together with the use of normalized filters, turns(4) into the simpler expression:

E[W 2v (n)] =

σ2u

1 + σ2u

E[z2B ] (5)

where E[z2B ] is the mean square value computed on the

generic block.

LenaL=1 L=2 L=4 L=16

noisy 12.11 14.90 17.84 23.79modified BM3D 27.08 29.27 31.16 34.40SA-WBMMAE 25.10 27.33 29.04 32.47PPB SAR 25it 26.68 28.45 29.88 32.70BM3D 26.46 29.21 31.26 34.52NLM 21.79 25.66 28.53 33.16PPB 25it 25.31 27.85 29.75 32.82

NapoliL=1 L=2 L=4 L=16

noisy 14.28 17.05 19.99 25.98modified BM3D 23.33 24.92 26.62 30.31SA-WBMMAE 22.05 23.41 24.78 27.74PPB SAR 25it 22.01 23.48 25.05 28.07BM3D 22.89 24.68 26.36 29.98NLM 21.31 23.65 25.66 28.92PPB 25it 21.74 23.39 25.07 28.18

Table 1. PSNR results for test images with simulated speckle.

4. EXPERIMENTAL RESULTS

We have investigated the performance of the proposed tech-nique with both natural images degraded by simulated specklenoise and actual SAR images. The first type of experimentallows us to compute a reliable quantitative measure of thealgorithm performance, something which is not possible withreal SAR images. We have selected the well-known image“Lena” to obtain results easily comparable with the litera-ture, and an aerial photograph of the city of Naples (Fig. 1),Italy, since it has statistics more similar to those of a SARimage. Results are compared with those of the most recenttechniques proposed for SAR image denoising, that is PPB-SAR [9] (nonlocal) and SA-WBMMAE [5] (local), as well aswith the nonlocal algorithms for AWGN images mentionedbefore (NLM, PPB, BM3D). For these last techniques, wecarry out preliminarily a log-transform, and then estimate andsubtract the non-zero mean [5] of the noise. In Tab. 4 we re-port PSNR results for Lena and Napoli corrupted by specklenoise in amplitude format (square-root intensity [14]) withdifferent number of looks. The proposed modified version ofBM3D provides almost always the best performance, betterthan all other SAR-oriented denoising techniques, especiallyfor the aerial image which more closely resembles an actualSAR image. A visual inspection of the filtered images furtherreinforces this point since the SAR-oriented PPB, despite itsgood PSNR level, outputs an unacceptably oversmoothed im-age, contrary to what happens with the proposed techniquewhich preserves accurately all details. Only with the low-noise versions of Lena (4 and 16 looks) the homomorphicBM3D behaves slightly better. Considering that somethingsimilar happens with the two versions of PPB, this seems toconfirm that with a large number of looks the log-transformed

(a) Noisy image (b) modified BM3D

(c) SA-WBMMAE (d) PPB SAR 25it

Fig. 1. Napoli L=1.

speckle is approximately gaussian [14], justifying the homo-morphic approach in this circumstances. In any case, the pro-posed SAR-oriented version behaves clearly better than allother techniques with a small number of looks, by far the mostcritical and interesting case.

Finally, we show results for a real amplitude, single lookTerraSar-X image from Infoterra taken over the Rosen (Ger-many) Fig. 2. As already said, assessing the performancefor actual SAR images is quite difficult, lacking a “clean”reference image, and measures like the equivalent numberof looks tell very little about detail preservation. Therefore,we prefer to rely on visual inspection to compare the dif-ferent techniques. Again, it seems safe to say that the pro-posed technique does a very good job, reducing significantlythe noise power without appreciably affecting image details,while competing techniques give rise to more noisy images(SA-WBMMAE) or oversmoothing phenomena (PPB-SAR).

5. CONCLUSIONS

In this work we introduce a modified version of BM3D forspeckle reduction, in which the hard thresholding step isreplaced by a local minimum mean square error shrinkagestrategy, and the distance, used in in block matching step, ischanged accordingly. This method turns out to be competitiveboth with state of art despeckling algorithm (i.e. [9]) and withthe original BM3D applied in an homomorphic framework.

Since in this work we leave the second step of BM3D un-

(a) Original image (b) modified BM3D

(d) SA-WBMMAE (e) PPB SAR 25it

Fig. 2. Rosen c©Infoterra GmbH

changed, further investigations will be devoted to the devel-opment of a fully homomorphic technique that comprises thesecond step too.

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