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

Abstract

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

Keywords

• Lp-norm regularization
• adaptive weighted
• iterative thresholding
• multiple dictionaries
• single–dictionary
• image restoration