Efficient Algorithms for Convolutional Sparse Representations
Abstract
When applying sparse representation techniques to images, the standard approach is to independently compute the representations for a set of overlapping image patches. This method performs very well in a variety of applications, but results in a representation that is multi-valued and not optimized with respect to the entire image. Additionally, an alternative representation structure is provided by a convolutional sparse representation, in which a sparse representation of an entire image is computed by replacing the linear combination of a set of dictionary vectors by the sum of a set of convolutions with dictionary filters. The resulting representation is both single-valued and jointly optimized over the entire image. While this form of a sparse representation has been applied to a variety of problems in signal and image processing and computer vision, the computational expense of the corresponding optimization problems has restricted application to relatively small signals and images. Here, this paper presents new, efficient algorithms that substantially improve on the performance of other recent methods, contributing to the development of this type of representation as a practical tool for a wider range of problems.
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program
- OSTI Identifier:
- 1471324
- Report Number(s):
- LA-UR-14-28830
Journal ID: ISSN 1057-7149
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- IEEE Transactions on Image Processing
- Additional Journal Information:
- Journal Volume: 25; Journal Issue: 1; Journal ID: ISSN 1057-7149
- Publisher:
- IEEE
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Sparse Representation; Sparse Coding; Dictionary Learning; Convolutional Sparse Representation; ADMM
Citation Formats
Wohlberg, Brendt Egon. Efficient Algorithms for Convolutional Sparse Representations. United States: N. p., 2015.
Web. doi:10.1109/TIP.2015.2495260.
Wohlberg, Brendt Egon. Efficient Algorithms for Convolutional Sparse Representations. United States. https://doi.org/10.1109/TIP.2015.2495260
Wohlberg, Brendt Egon. Tue .
"Efficient Algorithms for Convolutional Sparse Representations". United States. https://doi.org/10.1109/TIP.2015.2495260. https://www.osti.gov/servlets/purl/1471324.
@article{osti_1471324,
title = {Efficient Algorithms for Convolutional Sparse Representations},
author = {Wohlberg, Brendt Egon},
abstractNote = {When applying sparse representation techniques to images, the standard approach is to independently compute the representations for a set of overlapping image patches. This method performs very well in a variety of applications, but results in a representation that is multi-valued and not optimized with respect to the entire image. Additionally, an alternative representation structure is provided by a convolutional sparse representation, in which a sparse representation of an entire image is computed by replacing the linear combination of a set of dictionary vectors by the sum of a set of convolutions with dictionary filters. The resulting representation is both single-valued and jointly optimized over the entire image. While this form of a sparse representation has been applied to a variety of problems in signal and image processing and computer vision, the computational expense of the corresponding optimization problems has restricted application to relatively small signals and images. Here, this paper presents new, efficient algorithms that substantially improve on the performance of other recent methods, contributing to the development of this type of representation as a practical tool for a wider range of problems.},
doi = {10.1109/TIP.2015.2495260},
journal = {IEEE Transactions on Image Processing},
number = 1,
volume = 25,
place = {United States},
year = {Tue Oct 27 00:00:00 EDT 2015},
month = {Tue Oct 27 00:00:00 EDT 2015}
}
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