Hierarchical CoSaMP for compressively sampled sparse signals with nested structure

This paper presents a novel procedure, named Hierarchical Compressive Sampling Matching Pursuit (CoSaMP), for reconstruction of compressively sampled sparse signals whose coefficients are organized according to a nested structure. The Hierarchical CoSaMP is inspired by the CoSaMP algorithm, and it is based on a suitable hierarchical extension of the support over which the compressively sampled signal is reconstructed. We analytically demonstrate the convergence of the Hierarchical CoSaMP and show by numerical simulations that the Hierarchical CoSaMP outperforms state-of-the-art algorithms in terms of accuracy for a given number of measurements at a restrained computational complexity.