A Generalized Hard Thresholding Pursuit Algorithm

Compressed sensing ensures the accurate reconstruction of sparse signals from far fewer samples than required in the classical Shannon–Nyquist theorem. In this paper, a generalized hard thresholding pursuit (GHTP) algorithm is presented that can recover unknown vectors without the sparsity level information. We also analyze the convergence of the proposed algorithm. Numerical experiments are given for synthetic and real-world data to illustrate the validity and the good performance of the proposed algorithm.