A fast tree-based algorithm for Compressed Sensing with sparse-tree prior

In Compressed Sensing, the sparse representation property of an unknown signal in a certain basis has been used as the only prior knowledge for signal reconstruction from a limited number of measurements. Recently, more and more research has focused on model-based recovery algorithms, in which special structures of the unknown signal are exploited in addition to the sparse prior. A popular structure is the sparse-tree structure exhibited in the wavelet transform of piecewise smooth signals and in many practical models. In this paper, a reconstruction algorithm that exploits this sparse-tree prior, the Tree-based Orthogonal Matching Pursuit (TOMP) algorithm, is proposed and studied in detail. Theoretical analyses and empirical experiments show that the proposed algorithm gives reconstruction quality comparable with more sophisticated algorithms, while being much simpler.