Sparse Adaptive Iteratively-Weighted Thresholding Algorithm (SAITA) for
L
p
-Regularization Using the Multiple Sub-Dictionary Representation
Yunyi Li,
Jie Zhang,
Shangang Fan,
Jie Yang,
Jian Xiong,
Xiefeng Cheng,
Hikmet Sari,
Fumiyuki Adachi,
Guan Gui
Affiliations
Yunyi Li
College of Electronic and Optical Engineering & College of Microelectronics, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Jie Zhang
College of Telecommunication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Shangang Fan
College of Telecommunication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Jie Yang
College of Telecommunication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Jian Xiong
College of Telecommunication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Xiefeng Cheng
College of Electronic and Optical Engineering & College of Microelectronics, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Hikmet Sari
College of Telecommunication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Fumiyuki Adachi
Research Organization of Electrical Communication, Tohoku University, Sendai 980-8577, Japan
Guan Gui
College of Telecommunication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
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.
