Efficient ADMM-Based Algorithms for Convolutional Sparse Coding

Convolutional sparse coding improves on the standard sparse approximation by incorporating a global shift-invariant model. The most efficient convolutional sparse coding methods are based on the alternating direction method of multipliers and the convolution theorem. The only major difference betwee...

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Bibliographic Details
Published in:IEEE signal processing letters Vol. 29; pp. 389 - 393
Main Authors: Veshki, Farshad, Vorobyov, Sergiy
Format: Journal Article
Language:English
Published: New York IEEE 2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
alternating direction method of multipliers
Approximation
Approximation algorithms
Coding
constrained sparse approximation
Convolution
Convolutional codes
Convolutional sparse coding
Dictionaries
dictionary learning
Image coding
Machine learning
Mathematical analysis
Optimization
Signal processing algorithms
ISSN:1070-9908, 1558-2361
Online Access:Get full text
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Summary:Convolutional sparse coding improves on the standard sparse approximation by incorporating a global shift-invariant model. The most efficient convolutional sparse coding methods are based on the alternating direction method of multipliers and the convolution theorem. The only major difference between these methods is how they approach a convolutional least-squares fitting subproblem. In this letter, we present a novel solution for this subproblem, which improves the computational efficiency of the existing algorithms. The same approach is also used to develop an efficient dictionary learning method. In addition, we propose a novel algorithm for convolutional sparse coding with a constraint on the approximation error. Source codes for the proposed algorithms are available online.
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ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2021.3135196