Automatic threshold estimation for Iterative Shrinkage Algorithms used with compressed sensing

Recently, a new class of algorithms has been developed which iteratively build a sparse solution to an underdetermined linear system of equations. These algorithms are known in the literature as Iterative Shrinkage Algorithms (ISA). ISA algorithms depend on a thresholding parameter, which is usually provided by the user. In this paper we develop a new approach for automatically estimating this thresholding parameter. The proposed approach is general in a sense that it does not assume any distribution on the entries of the dictionary matrix, nor on the nonzero coefficients of the solution vector. In addition, the proposed approach is simple and can be adapted for use with newly evolving ISA algorithms. Moreover, the simulation results show that these proposed algorithms outperform their previous counterparts.