Patch-PCA denoising


Introduction

In recent years, overcomplete dictionaries combined with sparse learning techniques became extremely popular in computer vision. While their usefulness is undeniable, the improvement they provide in specific tasks of computer vision is still poorly understood. The aim of the present work is to demonstrate that for the task of image denoising, nearly state-of-the-art results can be achieved using small dictionaries only, provided that they are learned directly from the noisy image. We focus on two particular type of noise: Poisson and Gaussian noise.

Poisson noise reduction with non-local PCA (NL-PCA)
Photon limitations arise in spectral imaging, nuclear medicine, astronomy and night vision. The Poisson distribution used to model this noise has variance equal to its mean so blind application of standard noise removals methods yields significant artifacts. The aim of the present work is to demonstrate that for the task of image denoising, nearly state-of-the-art results can be achieved using small dictionaries only, provided that they are learned directly from the noisy image. To this end, we introduce patch-based denoising algorithms which perform an adaptation of PCA (Principal Component Analysis) for Poisson noise. The results reveal that, despite its simplicity, PCA-flavored denoising appears to be competitive with other state-of-the-art denoising algorithms.

(a) Noisy image (b) Reconstructed with our NL-PCA (c) Anscombe version of the algorithm
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Papers:
"Poisson Noise Reduction with Non-Local PCA",
J. Salmon, , and , ICASSP 2012, PDF

Corresponding Matlab DEMO and ZIP.

The long version of this paper, and a version of the code adding sparsity constraints on the coefficient of the decomposition is given in the NLSPCA page:
"Poisson Noise Reduction with Non-Local PCA",
J. Salmon, , , , submitted, 2012, PDF

Corresponding Matlab DEMO and ZIP.

Gaussian Patch-PCA (GP-PCA)

In this project we apply the idea of patch-based PCA in the case of Gaussian noise. We have mainly compare the efficiency of different procedure using PCA as a dictionary techniques. To this end, we introduce three patch-based denoising algorithms which perform hard thresholding on the coefficients of the patches in image-specific orthogonal dictionaries. The algorithms differ by the methodology of learning the dictionary: local PCA (PLPCA), hierarchical PCA (PHPCA) and global PCA (GHPCA). We carry out a comprehensive empirical evaluation of the performance of these algorithms in terms of accuracy and running times. The results reveal that, despite its simplicity, PCA-based denoising appears to be competitive with the state-of-the-art denoising algorithms, especially for large images and moderate signal-to-noise ratios.

(a) Local search windows (b) 16 first axes in window 1 (c) 16 first axes in window 2
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Papers:
"Image denoising with patch based PCA: local versus global"
C.-A. , J. Salmon, A. S. , BMVC 2011, PDF.

Corresponding Matlab DEMO and ZIP.

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