Projective Hard Thresholding Pursuit for Nonnegative Sparse Recovery

The data in scientific and engineering computations is usually gifted physical meaning in the presence of nonnegativity. For high performance and effectiveness, it is necessary and beneficial to consider the prior nonnegativity in processing the nonnegative information. In this paper, we propose a Projective Hard Thresholding Pursuit (PHTP) method for the nonnegative sparse signal recovery. It reconstructs sparse signal by combining the nonnegative projection with HTP. Theoretically, we prove that the proposed algorithm can find all nonnegative s-sparse signals provided the sensing matrix has suitable restricted isometry property. Moreover, We extend this result to its fast version. Besides, we verify PHTP's convergence with the measurement error being nonzero. Numerical experiments demonstrate that PHTP outperforms HTP and Nonnegative Least Squares (NNLS) for nonnegative sparse recovery and denoising.