Probabilistic PatchBased 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 NonLocal means (NL means) filter [2] to SAR images. Then, an efficient filter as been designed, able to cope with non Gaussian noise, multidimensionnal images and especially to the various existing SAR images. Results on the extended filter for amplitude SAR images are given on this page. The NLInSAR filter is also an extension of the nonlocal means based on the PPB filter for interferometric SAR images, as well as the Poisson NL means filter for images sensed in lowlight conditions.
 The NL means filter denoises an image by computing for each pixel s the mean of similar pixel values v_{t}. 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 v_{t} :
 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 Δ_{s} and Δ_{t} 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(v_{Δs}, v_{Δt}  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 patchbased 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."

CharlesAlban Deledalle, Loïc Denis and Florence Tupin,
Iterative Weighted Maximum Likelihood Denoising with Probabilistic PatchBased Weights,
IEEE Trans. on Image Processing, vol. 18, no. 12, pp. 26612672, December 2009 (download)

CharlesAlban Deledalle, Loïc Denis and Florence Tupin,
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 stateoftheart filters are proposed here : the BLSGSM filter [3], the KSVD filter [4], the BM3D filter [5] and the NLMeans filter [2]. In case of multiplicative speckle noise [1], five stateoftheart filters are proposed here : the Kuan filter [6], the WINSAR filter [7], the LMMSEUWD filter [8], the MAPUWD filter [9] and the MAPUWDS filter [10].
Quantitative Evaluation of the Denoising Algorithms
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 
BLSGSM  19.73  15.76  11.54  9.083 
KSVD  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 
BLSGSM  18.73  15.60  12.09  9.548 
KSVD  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 
BLSGSM  20.53  17.73  14.28  11.52 
KSVD  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 
BLSGSM  20.67  17.66  14.48  11.69 
KSVD  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 
WINSAR  8.819  10.48  12.04  15.82 
LLMMSEUWD  9.072  10.83  12.67  16.75 
MAPUWD  9.301  10.73  12.75  17.00 
MAPUWDS  9.645  11.44  13.28  16.93 
PPB nonit.  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 
WINSAR  8.568  10.65  12.14  15.17 
LLMMSEUWD  8.204  10.03  11.71  15.45 
MAPUWD  9.272  10.78  12.18  15.74 
MAPUWDS  9.257  10.68  12.31  15.71 
PPB nonit.  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 
WINSAR  8.689  11.42  13.15  16.24 
LLMMSEUWD  8.191  10.26  12.15  16.35 
MAPUWD  10.22  11.90  13.49  17.07 
MAPUWDS  10.34  11.97  13.72  17.24 
PPB nonit.  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 
WINSAR  10.35  13.00  14.72  17.90 
LLMMSEUWD  9.775  11.81  13.75  17.80 
MAPUWD  11.71  13.30  14.99  18.47 
MAPUWDS  11.87  13.53  15.14  18.65 
PPB nonit.  11.05  13.20  15.18  18.61 
PPB 25 it.  12.16  13.95  15.25  18.10 
Download the PPB filter
These pieces of Matlab software are based on C++ MexFunctions compiled for Linux 32bit, Linux 64bit 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 CharlesAlban Deledalle at deledalle (at) telecomparistech (dot) fr.
 PPB. filter for additive Gaussian noise [download],
 PPB. filter for multiplicative speckle noise, i.e NakagamiRayleigh distributions [download].
References
 Goodman, JW.
Some fundamental properties of speckle,
J. Opt. Soc. Am, vol. 66, no. 11, pp. 11451150, 1976.  Buades, A. and Coll, B. and Morel, J.M.
A NonLocal Algorithm for Image Denoising,
IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 2, 2005  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  Aharon, M. and Elad, M. and Bruckstein, A.
KSVD: An algorithm for designing overcomplete dictionaries for sparse representation,
IEEE Transactions on Signal Processing, 2006  Dabov, K. and Foi, A. and Katkovnik, V. and Egiazarian, K.
Image denoising by sparse 3D transformdomain collaborative filtering,
IEEE Transactions on Image Processing, 2007  Kuan, DT and Sawchuk, AA and Strand, TC and Chavel, P.
Adaptive noise smoothing filter for images with signaldependent noise,
IEEE Transactions on Pattern Analysis and Machine Intelligence, 1985  Achim, A. and Tsakalides, P. and Bezerianos, A.
SAR image denoising via Bayesian wavelet shrinkage based on heavytailed modeling
IEEE Transactions on Geoscience and Remote Sensing, 2003  Argenti, F. and Alparone, L.
Speckle removal from SAR images in the undecimated wavelet domain,
IEEE Transactions on Geoscience and Remote Sensing, 2002  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  Bianchi, T. and Argenti, F. and Alparone, L.
SegmentationBased MAP Despeckling of SAR Images in the Undecimated Wavelet Domain
IEEE Transactions on Geoscience and Remote Sensing, 2008
Last modified: Fri Apr 7 01:23:58 Europe/Berlin 2017