A reconstruction framework based on mixed sparse representations for compressive sensing

The theory of compressive sensing (CS) has been proposed for almost a decade, and massive experiments show that compressive sensing has favorable performance in signal processing. Assuming that a signal can be represented or approximated by only a few suitably chosen terms in a frame expansion, CS allows to recover this signal from much fewer samples than the Shannon-Nyquist theory requires. In general, a natural image can be regard as a combination of subimage of smooth, edges, and point-like components, respectively. Since each domain transformation method is capable of representing only a particular kind of ground object or texture, a group of domain transformations are used to sparsely represent each subimage. In this paper, a novel framework based on mixed sparse representations (MSRs) is proposed for solving the problem of CS image reconstruction. The split Bregman iteration is utilized in our framework for better performance both in terms of reconstruction quality and computational efficiency.