Sparse Adaptive Iteratively-Weighted Thresholding Algorithm (SAITA) for [Formula: see text]-Regularization Using the Multiple Sub-Dictionary Representation

Both [Formula: see text] and [Formula: see text] are two typical non-convex regularizations of [Formula: see text] ([Formula: see text]), which can be employed to obtain a sparser solution than the [Formula: see text] regularization. Recently, the multiple-state sparse transformation strategy has been developed to exploit the sparsity in [Formula: see text] regularization for sparse signal recovery, which combines the iterative reweighted algorithms. To further exploit the sparse structure of signal and image, this paper adopts multiple dictionary sparse transform strategies for the two typical cases [Formula: see text] based on an iterative [Formula: see text] thresholding algorithm and then proposes a sparse adaptive iterative-weighted [Formula: see text] thresholding algorithm (SAITA). Moreover, a simple yet effective regularization parameter is proposed to weight each sub-dictionary-based [Formula: see text] regularizer. Simulation results have shown that the proposed SAITA not only performs better than the corresponding [Formula: see text] algorithms but can also obtain a better recovery performance and achieve faster convergence than the conventional single-dictionary sparse transform-based [Formula: see text] case. Moreover, we conduct some applications about sparse image recovery and obtain good results by comparison with relative work.