An improved IRLS algorithm with double-threshold sigmoid penalty

The thresholding methods based on the generalized IRLS iteration are discussed under the complex-valued condition in this paper. An improved IRLS algorithm with double-threshold sigmoid (DTHS) penalty are proposed herein. It is shown that the generalized IRLS algorithm is unbiased if the thresholding penalty can eliminate the undesired perturbation term added on the correlation matrix of the measurement matrix. The test show that the new algorithms are endowed with stability and insensitivity with respect to the regularization parameter by selecting some sound upper thresholds, which can eliminate the undesired perturbation term added on the correlation matrix of the measurement matrix. Further analyses show that the DTHS-1 algorithm is suitable to deal with both of the sparse and continuous problems for the i.i.d random. The noise performance of the DTHS-1 algorithm is always superior to that of the IRLS algorithm.