Compressive Sensing via Nonlocal Low-Rank Regularization

• Published in: IEEE transactions on image processing Vol. 23; no. 8; pp. 3618 - 3632
• Main Authors: Dong, Weisheng, Shi, Guangming, Li, Xin, Ma, Yi, Huang, Feng
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Approximation methods; Biological and medical sciences; Brain - anatomy & histology; Computational efficiency; Computerized, statistical medical data processing and models in biomedicine; Data Compression - methods; Detection; Detection, estimation, filtering, equalization, prediction; Educational institutions; Exact sciences and technology; Fourier transforms; Humans; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Image reconstruction; Information, signal and communications theory; Magnetic resonance imaging; Magnetic Resonance Imaging - methods; Medical management aid. Diagnosis aid; Medical sciences; Minimization; Optimization; Pattern Recognition, Automated - methods; Reconstruction; Regularization; Reproducibility of Results; Sample Size; Sampling, quantization; Sensitivity and Specificity; Signal and communications theory; Signal processing; Signal Processing, Computer-Assisted; Signal, noise; Sparsity; Telecommunications and information theory; nonconvex optimization; low-rank approximation; Compresses sensing; structured sparsity; alternative direction multiplier method; Performance evaluation; State of the art; Non convex programming; Photographic image; Image processing; Image restoration; Algorithm; Nuclear magnetic resonance imaging; Implementation; Photography; Signal processing; Medical imagery; Alternative method; Signal reconstruction; Multiplying circuits; Compressed sensing
• ISSN: 1057-7149; 1941-0042; 1941-0042
• DOI: 10.1109/TIP.2014.2329449

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 technique. Experimental results have shown that the proposed NLR-CS algorithm can significantly outperform existing state-of-the-art CS techniques for image recovery.