Sparse Adaptive Iteratively-Weighted Thresholding Algorithm (SAITA) for Lp-Regularization Using the Multiple Sub-Dictionary Representation

Both L1/2 and L2/3 are two typical non-convex regularizations of Lp (0<p<1), which can be employed to obtain a sparser solution than the L₁ regularization. Recently, the multiple-state sparse transformation strategy has been developed to exploit the sparsity in L₁ 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 p∈{1/2, 2/3} based on an iterative Lp thresholding algorithm and then proposes a sparse adaptive iterative-weighted Lp thresholding algorithm (SAITA). Moreover, a simple yet effective regularization parameter is proposed to weight each sub-dictionary-based Lp regularizer. Simulation results have shown that the proposed SAITA not only performs better than the corresponding L₁ algorithms but can also obtain a better recovery performance and achieve faster convergence than the conventional single-dictionary sparse transform-based Lp case. Moreover, we conduct some applications about sparse image recovery and obtain good results by comparison with relative work.