![](/images/graphics-bg.png)
Convergence of Slice-Based Block Coordinate Descent Algorithm for Convolutional Sparse Coding
Joint Authors
Wang, Jin-Jia
Li, Jing
Yu, Hui
Wei, Xiao
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-07-30
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
Convolutional sparse coding (CSC) models are becoming increasingly popular in the signal and image processing communities in recent years.
Several research studies have addressed the basis pursuit (BP) problem of the CSC model, including the recently proposed local block coordinate descent (LoBCoD) algorithm.
This algorithm adopts slice-based local processing ideas and splits the global sparse vector into local vector needles that are locally computed in the original domain to obtain the encoding.
However, a convergence theorem for the LoBCoD algorithm has not been given previously.
This paper presents a convergence theorem for the LoBCoD algorithm which proves that the LoBCoD algorithm will converge to its global optimum at a rate of O1/k.
A slice-based multilayer local block coordinate descent (ML-LoBCoD) algorithm is proposed which is motivated by the multilayer basis pursuit (ML-BP) problem and the LoBCoD algorithm.
We prove that the ML-LoBCoD algorithm is guaranteed to converge to the optimal solution at a rate O1/k.
Preliminary numerical experiments demonstrate the better performance of the proposed ML-LoBCoD algorithm compared to the LoBCoD algorithm for the BP problem, and the loss function value is also lower for ML-LoBCoD than LoBCoD.
American Psychological Association (APA)
Li, Jing& Yu, Hui& Wei, Xiao& Wang, Jin-Jia. 2020. Convergence of Slice-Based Block Coordinate Descent Algorithm for Convolutional Sparse Coding. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-8.
https://search.emarefa.net/detail/BIM-1195173
Modern Language Association (MLA)
Li, Jing…[et al.]. Convergence of Slice-Based Block Coordinate Descent Algorithm for Convolutional Sparse Coding. Mathematical Problems in Engineering No. 2020 (2020), pp.1-8.
https://search.emarefa.net/detail/BIM-1195173
American Medical Association (AMA)
Li, Jing& Yu, Hui& Wei, Xiao& Wang, Jin-Jia. Convergence of Slice-Based Block Coordinate Descent Algorithm for Convolutional Sparse Coding. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-8.
https://search.emarefa.net/detail/BIM-1195173
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1195173