Compressed Sensing Recovery via Collaborative Sparsity

Compressed Sensing (CS) has drawn quite an amount of attention as a joint sampling and compression approach. Its theory shows that a signal can be decoded from many fewer measurements than suggested by the Nyquist sampling theory, when the signal is sparse in some domain. So one of the most significant challenges in CS is to seek a domain where a signal can exhibit a high degree of sparsity and hence be recovered faithfully. Most of conventional CS recovery approaches, however, exploited a set of fixed bases (e.g. DCT, wavelet and gradient domain) for the entirety 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 compressed sensing recovery via collaborative sparsity (RCoS), which enforces local two-dimensional sparsity and nonlocal three-dimensional sparsity simultaneously in an adaptive hybrid space-transform domain, thus substantially utilizing intrinsic sparsities 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 demonstrate the efficacy of the new CS recovery strategy.