Open AccessA linearly convergent proximal ADMM with new iterative format for BPDN in compressed sensing problem
Author(s) -
Bing Xue,
Jiakang Du,
Huaijiang Sun,
Yiju Wang
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022586
Subject(s) - dimension (graph theory) , compressed sensing , convergence (economics) , algorithm , rate of convergence , inference , reduction (mathematics) , basis (linear algebra) , computer science , mathematics , basis pursuit , iterative method , mathematical optimization , artificial intelligence , key (lock) , combinatorics , matching pursuit , economics , economic growth , geometry , computer security
In recent years, compressive sensing (CS) problem is being popularly applied in the fields of signal processing and statistical inference. The alternating direction method of multipliers (ADMM) is applicable to the equivalent forms of basis pursuit denoising (BPDN) in CS problem. However, the solving speed and accuracy are adversely affected when the dimension increases greatly. In this paper, a new iterative format of proximal ADMM, which has fast solving speed and pinpoint accuracy when the dimension increases, is proposed to solve BPDN problem. Global convergence of the new type proximal ADMM is established in detail, and we exhibit a $ R- $ linear convergence rate under suitable condition. Moreover, we apply this new algorithm to solve different types of BPDN problems. Compared with the state-of-the-art of algorithms in BPDN problem, the proposed algorithm is more accurate and efficient.