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 . The detail is given here  and source-code webpage Thanks you for your wonderful CS webpageBest regards,Thuong Nguyen--Master course at Digital Media Lab.College of Information and Communication EngineeringSungkyunkwan 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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