Reconstruction algorithm using exact tree projection for tree‐structured compressive sensing

Abstract

Tree-structured compressive sensing (CS) shows that it is possible to recover tree-sparse signals using fewer measurements compared with conventional CS. However, performance guarantees rely heavily on the premise that an exact tree projection (ETP) algorithm is employed. Nevertheless, for a given sparsity, the condensing sort and select algorithm in the model-based compressive sampling matching pursuit (CoSaMP) algorithm can only yield an approximate tree projection. Therefore, in order to ensure reconstruction precision, the authors propose the combination of an ETP algorithm with the CoSaMP algorithm. Further, the hierarchical wavelet connected tree is also integrated into the ETP-CoSaMP algorithm to offset the high computational complexity of the ETP algorithm. Experimental results indicate that the hierarchical ETP based on CoSaMP algorithm (HETP-CoSaMP algorithm) enhances reconstruction accuracy while retaining reconstruction time that is comparable with that of the model-based CoSaMP algorithm.