Probabilistic Patch-Based filter

• Description of the filter
• Qualitative Evaluation of the Denoising Algorithms
• Quantitative Evaluation of the Denoising Algorithms
• Download the PPB filter
• References

Description of the filter

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• A full description of the probabilistic patch-based filter is available in the following article:
  

  Charles-Alban Deledalle, Loïc Denis and Florence Tupin,
  Iterative Weighted Maximum Likelihood Denoising with Probabilistic Patch-Based Weights,
  IEEE Trans. on Image Processing, to appear (download)

• 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 espacially to the various existing SAR images.
• The NL means filter denoises an image by computing for each pixel s the mean of similar pixel values u_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 by computing the weighted maximum likelihood from the pixel values u_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 λ is an arbitrary positive real and h is a filtering parameter. The similarity probability can be decomposed with two terms, the similarity likelihood on one hand p(u_Δs, u _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.

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.

Quantitative Evaluation of the Denoising Algorithms

Download the PPB filter

These Matlab softwares are based on C++ Mex-Functions compiled for Linux architectures (32-bit CPU). Matlab script exemples are given, they have been written for MATLAB Version 7.4.0.336 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.

• PPB. filter for additive Gaussian noise [Linux Matlab software],
• PPB. filter for multiplicative speckle noise (Nakagami-Rayleigh distribution) [Linux Matlab software].

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