Nonconvex Weighted \ell p Minimization Based Group Sparse Representation Framework for Image Denoising

Nonlocal image representation or group sparsity has attracted considerable interest in various low-level vision tasks and has led to several state-of-the-art image denoising techniques, such as BM3D, learned simultaneous sparse coding. In the past, convex optimization with sparsity-promoting convex...

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Bibliographic Details
Published in:IEEE signal processing letters 2017-11, Vol.24 (11), p.1686-1690
Main Authors: Wang, Qiong, Zhang, Xinggan, Wu, Yu, Tang, Lan, Zha, Zhiyuan
Format: Article
Language:English
Subjects:
Adaptive patch search (APS)
Dictionaries
generalized soft-thresholding (GST) algorithm
group sparsity
Image denoising
Minimization
Noise measurement
Noise reduction
Signal processing algorithms
Sparse matrices
weighted <named-content xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" content-type="math" xlink:type="simple"> <inline-formula> <tex-math notation="LaTeX"> ell _p</tex-math> </inline-formula> </named-content> minimization
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Summary:Nonlocal image representation or group sparsity has attracted considerable interest in various low-level vision tasks and has led to several state-of-the-art image denoising techniques, such as BM3D, learned simultaneous sparse coding. In the past, convex optimization with sparsity-promoting convex regularization was usually regarded as a standard scheme for estimating sparse signals in noise. However, using convex regularization cannot still obtain the correct sparsity solution under some practical problems including image inverse problems. In this letter, we propose a nonconvex weighted ℓ p minimization based group sparse representation framework for image denoising. To make the proposed scheme tractable and robust, the generalized soft-thresholding algorithm is adopted to solve the nonconvex ℓ p minimization problem. In addition, to improve the accuracy of the nonlocal similar patch selection, an adaptive patch search scheme is proposed. Experimental results demonstrate that the proposed approach not only outperforms many state-of-the-art denoising methods such as BM3D and weighted nuclear norm minimization, but also results in a competitive speed.
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2017.2731791