Tree-Based Orthogonal Matching Pursuit Algorithm for Signal Reconstruction

Recent studies in linear inverse problems have recognized the sparse representation of unknown signal in a certain basis as an useful and effective prior information to solve those problems. In many multiscale bases (e.g. wavelets), signals of interest (e.g. piecewise-smooth signals) not only have few significant coefficients, but also those significant coefficients are well-organized in trees. We propose to exploit this sparse tree representation as additional prior information for linear inverse problems with limited numbers of measurements. In particular, our proposed algorithm named tree-based orthogonal matching pursuit (TOMP) is shown to provide significant better reconstruction compared to methods that only use sparse representation assumption.