Tree-Based Majorize-Maximize Algorithm for Compressed Sensing with Sparse-Tree Prior

Recent studies have shown that sparse representation can be used effectively as a prior in linear inverse problems. However, 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, named sparse-tree, prior for linear inverse problems with limited numbers of measurements. In particular, we present the tree-based majorize-maximize (TMM) algorithm for signal reconstruction in this setting. Our numerical results show that TMM provides significantly better reconstruction quality compared to the majorize-maximize (MM) algorithm that relies only on the sparse prior.