Signal Reconstruction using Sparse Tree Representations

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 the tree-structured sparse representation as additional prior information for linear inverse problems with limited numbers of measurements. We present numerical results showing that exploiting the sparse tree representations lead to better reconstruction while requiring less time compared to methods that only assume sparse representations.