Efficient Sparse Recovery With Arctangent Regularization: A Novel Iterative Thresholding Algorithm

被引:0
作者
He, Zihao [1 ]
Shu, Qianyu [2 ]
Wen, Jinming [1 ]
Cheung So, Hing [3 ]
机构
[1] Jinan Univ, Dept Informat Sci & Technol, Guangzhou 510632, Peoples R China
[2] Sichuan Normal Univ, Sch Math Sci, Chengdu 610066, Peoples R China
[3] City Univ Hong Kong, Dept Elect Engn, Hong Kong, Peoples R China
基金
中国国家自然科学基金;
关键词
Approximation algorithms; Vectors; Iterative algorithms; Convex functions; Convergence; Tensors; Sensors; Polynomials; Noise; Costs; Compressed sensing; thresholding algorithm; arctangent penalty; sparse recovery; L-1/2; REGULARIZATION; VARIABLE SELECTION; MINIMIZATION; CONVERGENCE;
D O I
10.1109/TCSVT.2024.3524668
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
Several existing works have revealed the effectiveness of arctangent-type penalties in exploiting sparsity for compressed sensing. However, addressing the subproblems associated with the arctangent penalty incurs considerable computational cost. Aiming to reduce complexity, we derive the closed-form proximity operator of an arctangent penalty, which is expressed as hyperbolic functions of sine and cosine in this paper. Accordingly, a computationally-efficient arctangent regularization iterative thresholding (ARIT) algorithm for sparse approximation is proposed. Furthermore, we theoretically prove that under certain conditions, the ARIT algorithm converges to a local minimizer of the arctangent regularization problem with an eventually linear convergence. Extensive experiments are conducted to compare our scheme with conventional iterative thresholding algorithms, demonstrating the former superiority in terms of the probability of successful recovery, rate of support recovery, phase transition, and robustness to noise.
引用
收藏
页码:5367 / 5379
页数:13
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