Image Compressive Sensing Recovery via Collaborative Sparsity

Abstract—Compressive sensing (CS) has drawn quite an amount of attention as a joint sampling and compression approach. Its theory shows that when the signal is sparse enough in some domain, it can be decoded from many fewer measurements than suggested by the Nyquist sampling theory. So one of the most challenging re-searches in CS is to seek a domain where a signal can exhibit a high degree of sparsity and hence be recovered faithfully. Most of the conventional CS recovery approaches, however, exploited a set of fixed bases (e.g., DCT, wavelet, and gradient domain) for the en-tirety of a signal, which are irrespective of the nonstationarity of natural signals and cannot achieve high enough degree of sparsity, thus resulting in poor rate-distortion performance. In this paper, we propose a new framework for image compressive sensing re-covery via collaborative sparsity, which enforces local 2-D sparsity and nonlocal 3-D sparsity simultaneously in an adaptive hybrid space-transformdomain, thus substantially utilizing intrinsic spar-sity of natural images and greatly confining the CS solution space. In addition, an efficient augmented Lagrangian-based technique is developed to solve the above optimization problem. Experimental results on a wide range of natural images are presented to demon-strate the efficacy of the new CS recovery strategy. Index Terms—Augmented Lagrangian, compressive sensing (CS), image recovery, sparsity