NLR-CS : Compressive Sensing via Nonlocal Low-rank Regularization - implementation -

Thuong Nguyen Canh just sent me the following:

Dear Igor,

I just go around the internet and found this paper on TIP which also include the implementation.  The expriment result quite good even better than the recent paper [1].  The detail is given here [2] and source-code webpage [3]

[1] http://nuit-blanche.blogspot.kr/2014/05/group-based-sparse-representation-for.html

[2]http://see.xidian.edu.cn/faculty/wsdong/Papers/Journal/TIP-11154-2013-final-double.pdf

[3] http://see.xidian.edu.cn/faculty/wsdong/NLR_Exps.htm

Thanks you for your wonderful CS webpage

Best regards,

Thuong Nguyen

--

Thuong Nguyen Canh

Master course at Digital Media Lab.

College of Information and Communication Engineering

Sungkyunkwan University

Thanks Thuong Nguyen !

If I am not mistaken, this is the first time I see an implementation made available of a low rank minimization that uses the log-det functional instead of the convex, and widely used, nuclear norm.

Compressive Sensing via Nonlocal Low-rank Regularization by Weisheng Dong, Guangming Shi, Xin Li, Yi Ma, and Feng Huang

Abstract— Sparsity has been widely exploited for exact reconstruction of a signal from a small number of random measurements. Recent advances have suggested that structured or group sparsity often leads to more powerful signal reconstruction techniques in various compressed sensing (CS) studies. In this paper, we propose a nonlocal low-rank regularization (NLR) approach toward exploiting structured sparsity and explore its application into CS of both photographic and MRI images. We also propose the use of a nonconvex log det(X) as a smooth surrogate function for the rank instead of the convex nuclear norm; and justify the benefit of such a strategy using extensive experiments. To further improve the computational efficiency of the proposed algorithm, we have developed a fast implementation using the alternative direction multiplier method (ADMM) technique. Experimental results have shown that the proposed NLR-CS algorithm can significantly outperform existing state-of-the-art CS techniques for image recovery.

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