Nonlocal Image Restoration With Bilateral Variance Estimation: A Low-Rank Approach

Abstract

Simultaneous sparse coding (SSC) or nonlocal image representation has shown great potential in various low-level vision tasks, leading to several state-of-the-art image restoration techniques, including BM3D and LSSC. However, it still lacks a physically plausible explanation about why SSC is a better model than conventional sparse coding for the class of natural images. Meanwhile, the problem of sparsity optimization, especially when tangled with dictionary learning, is computationally difficult to solve. In this paper, we take a low-rank approach toward SSC and provide a conceptually simple interpretation from a bilateral variance estimation perspective, namely that singular-value decomposition of similar packed patches can be viewed as pooling both local and nonlocal information for estimating signal variances. Such perspective inspires us to develop a new class of image restoration algorithms called spatially adaptive iterative singular-value thresholding (SAIST). For noise data, SAIST generalizes the celebrated BayesShrink from local to nonlocal models; for incomplete data, SAIST extends previous deterministic annealing-based solution to sparsity optimization through incorporating the idea of dictionary learning. In addition to conceptual simplicity and computational efficiency, SAIST has achieved highly competent (often better) objective performance compared to several state-of-the-art methods in image denoising and completion experiments. Our subjective quality results compare favorably with those obtained by existing techniques, especially at high noise levels and with a large amount of missing data.

Hyperspectral Image Super-Resolution via Nonlocal Low-Rank Tensor Approximation and Total Variation Regularization

“…Nonlocal self-similarity [30][31][32] is a patch-based useful prior, which means that, for a given local patch in one image, there are many patches similar to it. Motivated by [33], separating X into a set of image patches Ω = {X n ∈ R b×b×B } P p=1 (where b is the patch size, P is the number of 3D patches with overlap), and by performing block matching [34], a group of patches that is most similar to each patch X p can be extracted.…”

Non-Convex Low-Rank Approximation for Image Denoising and Deblurring

“…This assumption is validated by Wang et al, [17] where they called it the nonlocal spectral prior. In [1], Dong et al, combined NNM and L 2,1 −norm group sparsity for image restoration, and demonstrated very competitive results. In [2], a simultaneous sparse coding (SSC) scheme was proposed to code similar patches simultaneously and achieved impressive restoration results.…”

“…In various low-level vision tasks such as image restoration, the matrix formed by nonlocal similar patches collected from natural images is of low-rank, i.e., the low-rank prior exists to characterize the nonlocal self-similarity for a wide range of natural images [1]- [3]. Although a flurry of studies on low-rank matrix approximation have been reported due to the rapid development of convex and non-convex optimization techniques, comparatively little attention has been paid to low-level vision.…”

An adaptive parameter estimation for guided filter based image deconvolution

“…A nonlocally centralized sparse representation (NCSR) method is proposed in [18], it centralizes the sparse coding coefficients of the blurred image to enhance the performance of image deconvolution. Low-rank modeling based methods have also achieved great success in image deconvolution [23], [24], [25]. Since the property of image nonlocal self-similarity, similar patches are grouped in a low-rank matrix, then the matrix completion is performed each patch group to recover the image.…”