Key parameters for iterative thresholding-type algorithm with nonconvex regularization

Iterative thresholding-type algorithm, as one of the typical methods of compressed sensing (CS) theory, is widely used in sparse recovery field, because of its simple computational process. However, the estimation accuracy and convergence speed achieved by this type of algorithm with a nonconvex regularization, e.g., iterative half thresholding (IHalfT) algorithm, are not satisfactory, which limits its practical application. To improve the performance, a modified algorithm is proposed in this paper. Firstly, a novel non-negative expression is introduced in the algorithm to reduce the gap between the relaxation function and the objective function, which can bring tens of dB estimation accuracy improvement, and the convergence of the modified algorithm is verified. Secondly, the fundamental reasons for the remarkable improvement of performance are discussed and analyzed through theoretical derivation. Thirdly, the applicable conditions are elaborated for the modified algorithm. Finally, extensive experimental results demonstrate the effectiveness of the modified iterative thresholding-type algorithm with nonconvex regularization.