Image denoising using group sparsity residual and external nonlocal self-similarity prior

Abstract

Nonlocal image representation has been successfully used in many image-related inverse problems including denoising, deblurring and deblocking. However, a majority of reconstruction methods only exploit the nonlocal self-similarity (NSS) prior of the degraded observation image, it is very challenging to reconstruct the latent clean image. In this paper we propose a novel model for image denoising via group sparsity residual and external NSS prior. To boost the performance of image denoising, the concept of group sparsity residual is proposed, and thus the problem of image denoising is transformed into one that reduces the group sparsity residual. Due to the fact that the groups contain a large amount of NSS information of natural images, we obtain a good estimation of the group sparse coefficients of the original image by the external NSS prior based on Gaussian Mixture model (GMM) learning and the group sparse coefficients of noisy image is used to approximate the estimation. Experimental results have demonstrated that the proposed method not only outperforms many state-of-the-art methods, but also delivers the best qualitative denoising results with finer details and less ringing artifacts.Index Terms-Image denoising, group sparsity residual, nonlocal self-similarity, Gaussian Mixture model.

Group Sparsity Residual with Non-Local Samples for Image Denoising

“…Moreover, the computation speed of this method is very slow. Therefore, the proposed GSR-NLS is more reasonable and generic while providing very similar results as in [31,32].…”

“…Now we discuss the difference between the proposed GSR-NLS method, and NCSR [30] and our previous approaches [31,32].…”

“…In other words, if the pre-filtering cannot be used, the denoising method will fail. Our another work [32] estimated B from example image set based on GMM [34]. However, under many practical situations, the example image set is simply unavailable.…”

“…In general, there are a variety of methods to estimate Bi, which depends on the prior knowledge of the original image y. Different from [31,32], in this paper, based on the fact that natural images often contain repetitive structures [28], we search nonlocal similar patches (i.e., non-local samples) to the given patch and use the method similar to nonlocal means [8] to estimate Bi. Specifically, a good estimation of bi,1 can be computed by the weighted average of each element ai,j in Ai associated with each group including m nonlocal similar patches, where bi,1 and ai,j represent the first and the j-th element of Bi and Ai, respectively.…”

“…Most recently, the group sparsity residual [31,32] has been proposed for image denoising, which adopts a reference in each iteration to approximate the true sparse coefficients of each group. The reference was estimated by Gaussian mixture model (GMM) [22,34] or other algorithms, which is either not accurate or too slow.…”