SCIHTBB: Sparsity constrained iterative hard thresholding with Barzilai–Borwein step size

Iterative hard thresholding (IHT) is a class of effective methods to compute sparse solution for underdetermined linear system. In this paper, an efficient IHT method with theoretical guarantee is proposed and named SCIHTBB with attractive features: (1) Monotone and Non-Monotone versions are presented with initial Barzilai–Borwein step size and finite step line search. (2) Convergence analysis has been developed based on the asymmetrical restricted isometry property. (3) An adaptive sparsity framework is provided to tackle the problem with unknown sparsity. (4) Some extensions are presented to handle group sparsity, non-negative sparsity and matrix rank minimization. Experimental comparisons with some state of the art methods verify that SCIHTBB is faster and more accurate for compressive sensing and matrix completion.