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# Probabilistic Patch-Based filter (PPB)

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### Description of the filter

• This work has been achieved by Charles Deledalle supervised by Florence Tupin and Loïc Denis. The aim was to adapt the Non-Local means (NL means) filter [2] to SAR images. Then, an efficient filter as been designed, able to cope with non Gaussian noise, multi-dimensionnal images and especially to the various existing SAR images. Results on the extended filter for amplitude SAR images are given on this page. The NL-InSAR filter is also an extension of the non-local means based on the PPB filter for interferometric SAR images, as well as the Poisson NL means filter for images sensed in low-light conditions.
• The NL means filter denoises an image by computing for each pixel s the mean of similar pixel values vt. The similarity is measured with respect to the Euclidean distance between the neightbourhood of the pixels s and t. The Euclidean distance is well adapted to images corrupted by an additive white Gaussian noise.

The NL means algorithm computes the mean for all pixel s of the values of the pixels t weighted with respect to the similarity between two windows centered respectively on s and t
• To extend the filter to non Gaussian noise, we propose to estimate for each pixel s the underline image parameter θ* by computing the weighted maximum likelihood from the pixel values vt :
• where the weight w(s,t) defines the similarity between the pixels s and t. Based on the NL means filter assumptions, we define this weight by the similarity between two patches Δs and Δt centred respectively around s and t. This similarity is assumed to be linked to the similarity probability :
• where h is a filtering parameter. The similarity probability can be decomposed with two terms, the similarity likelihood on one hand p(vΔs, vΔt | θ*Δs = θ*Δt), and the prior similarity on the other hand p(θ*Δs = θ*Δt) which is modeled by using a previous estimation of the denoised image.
• A full description of the probabilistic patch-based filter is available in the following article:

Some of the publications below have appeared in an IEEE journal or conference record. By allowing you to download them, I am required to post the following copyright reminder: "This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder."

• Charles-Alban Deledalle, Loïc Denis and Florence Tupin,
Iterative Weighted Maximum Likelihood Denoising with Probabilistic Patch-Based Weights,
IEEE Trans. on Image Processing, vol. 18, no. 12, pp. 2661-2672, December 2009 (download)
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### Qualitative Evaluation of the Denoising Algorithms

• This tool ables to compare different denoising methods with the PPB filter. In case of additive White Gaussian Noise (WGN), four state-of-the-art filters are proposed here : the BLS-GSM filter [3], the K-SVD filter [4], the BM3D filter [5] and the NL-Means filter [2]. In case of multiplicative speckle noise [1], five state-of-the-art filters are proposed here : the Kuan filter [6], the WIN-SAR filter [7], the LMMSE-UWD filter [8], the MAP-UWD filter [9] and the MAP-UWD-S filter [10].
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(a) From top to bottom, corrupted images of Lena, by an additive WGN with standard deviation σ = 40. Denoised images using (a) Noisy (b) BM3D (c) PPB 25 it.
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(a) From top to bottom, corrupted images of Lena, by a multiplicative GSN with equivalent number of looks L = 3. Denoised images using (a) Noisy (b) MAP-UWD-S (c) PPB 25 it.
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(a) From top to bottom, SAR images of Bayard ©DGA ©ONERA, by a multiplicative GSN with equivalent number of looks L = 3. Denoised images using (a) Noisy (b) MAP-UWD-S (c) PPB 25 it.

Synthetic images:
Noise-free image:
Multiplicative GSN:
Real SAR images:
Noisy image:
Denoising methods:
Multiplicative GSN:
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### Quantitative Evaluation of the Denoising Algorithms

TABLE I
SNR values of estimated images using different denoising methods for images corrupted by (left) an additive WGN with different standard deviations and by (right) a multiplicative Goodman's speckle noise with different equivalent number of looks
 σ = 10 σ = 20 σ = 40 σ = 60 Barbara Noisy image 14.73 8.804 3.090 0.043 BLS-GSM 19.73 15.76 11.54 9.083 K-SVD 21.02 17.43 13.01 9.285 BM3D 21.48 18.38 14.59 12.14 NL means 19.85 16.97 12.85 10.24 PPB 25 it 18.69 15.96 13.49 10.99 Boat Noisy image 13.41 7.424 1.627 -1.490 BLS-GSM 18.73 15.60 12.09 9.548 K-SVD 18.87 15.62 11.78 9.039 BM3D 19.09 16.09 12.83 10.55 NL means 17.59 14.63 11.06 8.959 PPB 25 it 17.19 14.51 11.63 9.503 House Noisy image 13.27 7.263 1.445 -1.617 BLS-GSM 20.53 17.73 14.28 11.52 K-SVD 21.15 18.31 14.36 10.22 BM3D 21.77 18.94 15.78 13.28 NL means 20.25 17.55 13.33 10.40 PPB 25 it 19.59 17.03 14.20 11.57 Lena Noisy image 13.59 7.597 1.814 -1.251 BLS-GSM 20.67 17.66 14.48 11.69 K-SVD 20.93 17.81 14.18 11.09 BM3D 21.27 18.42 15.33 13.05 NL means 20.12 17.10 13.66 11.33 PPB 25 it 19.50 16.90 14.20 11.99
 L = 1 L = 2 L = 4 L = 16 Barbara Noisy image -1.090 1.694 4.611 10.57 Kuan 6.937 8.489 10.19 14.41 WIN-SAR 8.819 10.48 12.04 15.82 LLMMSE-UWD 9.072 10.83 12.67 16.75 MAP-UWD 9.301 10.73 12.75 17.00 MAP-UWD-S 9.645 11.44 13.28 16.93 PPB non-it. 9.785 11.88 14.05 17.83 PPB 25 it 10.58 12.51 13.98 16.59 Boat Noisy image -2.992 -0.179 2.696 8.667 Kuan 6.171 7.950 9.796 13.77 WIN-SAR 8.568 10.65 12.14 15.17 LLMMSE-UWD 8.204 10.03 11.71 15.45 MAP-UWD 9.272 10.78 12.18 15.74 MAP-UWD-S 9.257 10.68 12.31 15.71 PPB non-it. 8.708 10.49 12.22 15.33 PPB 25 it 9.426 10.91 12.25 15.10 House Noisy image -3.549 -0.760 2.113 8.096 Kuan 5.946 7.840 9.712 13.89 WIN-SAR 8.689 11.42 13.15 16.24 LLMMSE-UWD 8.191 10.26 12.15 16.35 MAP-UWD 10.22 11.90 13.49 17.07 MAP-UWD-S 10.34 11.97 13.72 17.24 PPB non-it. 9.064 11.61 14.29 18.27 PPB 25 it. 10.46 12.98 14.50 17.42 Lena Noisy image -2.449 0.343 3.249 9.188 Kuan 7.350 9.201 11.22 15.54 WIN-SAR 10.35 13.00 14.72 17.90 LLMMSE-UWD 9.775 11.81 13.75 17.80 MAP-UWD 11.71 13.30 14.99 18.47 MAP-UWD-S 11.87 13.53 15.14 18.65 PPB non-it. 11.05 13.20 15.18 18.61 PPB 25 it. 12.16 13.95 15.25 18.10

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We recommend to use the more recent NL-SAR technique for speckle noise reduction (available here: NL-SAR)

These pieces of Matlab software are based on C++ Mex-Functions compiled for Linux 32-bit, Linux 64-bit and Windows 32 bit. Matlab script exemples are given, they have been written for MATLAB with the Image Processing Toolbox (to load the images). Please refer to the REAME file for more details. For any comment, suggestion or question please contact Charles-Alban Deledalle at deledalle (at) telecom-paristech (dot) fr.

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### References

1. Goodman, JW.
Some fundamental properties of speckle,
J. Opt. Soc. Am, vol. 66, no. 11, pp. 1145-1150, 1976.
2. Buades, A. and Coll, B. and Morel, J.M.
A Non-Local Algorithm for Image Denoising,
IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2, 2005
3. Portilla, J. and Strela, V. and Wainwright, MJ and Simoncelli, EP
Image denoising using scale mixtures of Gaussians in the wavelet domain,
IEEE Transactions on Image Processing, 2003
4. Aharon, M. and Elad, M. and Bruckstein, A.
K-SVD: An algorithm for designing overcomplete dictionaries for sparse representation,
IEEE Transactions on Signal Processing, 2006
5. Dabov, K. and Foi, A. and Katkovnik, V. and Egiazarian, K.
Image denoising by sparse 3-D transform-domain collaborative filtering,
IEEE Transactions on Image Processing, 2007
6. Kuan, DT and Sawchuk, AA and Strand, TC and Chavel, P.
Adaptive noise smoothing filter for images with signal-dependent noise,
IEEE Transactions on Pattern Analysis and Machine Intelligence, 1985
7. Achim, A. and Tsakalides, P. and Bezerianos, A.
SAR image denoising via Bayesian wavelet shrinkage based on heavy-tailed modeling
IEEE Transactions on Geoscience and Remote Sensing, 2003
8. Argenti, F. and Alparone, L.
Speckle removal from SAR images in the undecimated wavelet domain,
IEEE Transactions on Geoscience and Remote Sensing, 2002
9. Argenti, F. and Bianchi, T. and Alparone, L.
Multiresolution MAP despeckling of SAR images based on locally adaptive generalized Gaussian pdf modeling
IEEE Transactions on Image Processing, 2006
10. Bianchi, T. and Argenti, F. and Alparone, L.
Segmentation-Based MAP Despeckling of SAR Images in the Undecimated Wavelet Domain
IEEE Transactions on Geoscience and Remote Sensing, 2008
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 In France (currently out of this office): Charles Deledalle - charles-alban (dot) deledalle (at) math.u-bordeaux (dot) fr Bureau 209 Institut de Mathématiques de Bordeaux Université Bordeaux 351, cours de la Libération - F-33405 TALENCE cedex FRANCE +33 (0)5 40 00 21 14 In USA (currently at this office): Charles Deledalle - cdeledalle (at) ucsd (dot) edu Jacobs Hall, Room 4808 Jacobs School of Engineering University of California, San Diego 9500 Gilman Drive La Jolla, CA 92093 USA