Convergence of Slice-Based Block Coordinate Descent Algorithm for Convolutional Sparse Coding

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)...

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Published in:Mathematical problems in engineering Vol. 2020; no. 2020; pp. 1 - 8
Main Authors: Wang, Jin-Jia, Wei, Xiao, Yu, Hui, Li, Jing
Format: Journal Article
Language:English
Published: Cairo, Egypt Hindawi Publishing Corporation 2020
Hindawi
John Wiley & Sons, Inc
Subjects:
Algorithms
Coding
Convergence
Descent
Dictionaries
Image processing
Mathematical problems
Methods
Multilayers
Needles
Optimization
Signal processing
Theorems
Variables
ISSN:1024-123X, 1563-5147
Online Access:Get full text
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Summary: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.
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ISSN:1024-123X
1563-5147
DOI:10.1155/2020/4367515