A Sufficient Condition for Low-Rank Recovery via Iterative Hard Thresholding Pursuit

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In this pape, we propose a matrix Iterative Hard thresholding pursuit algorithm for low-rank minimization that extends Foucart's Hard Thresholding Pursuit (HTP) algorithm from the sparse vector to the low-rank matrix case. The performance guarantee is given in terms of the rank-restricted isometry property and a low-rank solotion is presented. The numerical experiments empirically demonstrate that, although the affine constraints does not satisfy the restricted isometry property in matrix completion, our algorithm also recovers the low-rank matrix from a number of uniformly sampled entries and is more efficient compared with SVT and ADMiRA.