Efficient convolutional sparse coding
Abstract
Computationally efficient algorithms may be applied for fast dictionary learning solving the convolutional sparse coding problem in the Fourier domain. More specifically, efficient convolutional sparse coding may be derived within an alternating direction method of multipliers (ADMM) framework that utilizes fast Fourier transforms (FFT) to solve the main linear system in the frequency domain. Such algorithms may enable a significant reduction in computational cost over conventional approaches by implementing a linear solver for the most critical and computationally expensive component of the conventional iterative algorithm. The theoretical computational cost of the algorithm may be reduced from O(M.sup.3N) to O(MN log N), where N is the dimensionality of the data and M is the number of elements in the dictionary. This significant improvement in efficiency may greatly increase the range of problems that can practically be addressed via convolutional sparse representations.
- Inventors:
- Issue Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1364429
- Patent Number(s):
- 9,684,951
- Application Number:
- 14/668,900
- Assignee:
- Los Alamos National Security, LLC
- DOE Contract Number:
- AC52-06NA25396
- Resource Type:
- Patent
- Resource Relation:
- Patent File Date: 2015 Mar 25
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING
Citation Formats
Wohlberg, Brendt. Efficient convolutional sparse coding. United States: N. p., 2017.
Web.
Wohlberg, Brendt. Efficient convolutional sparse coding. United States.
Wohlberg, Brendt. Tue .
"Efficient convolutional sparse coding". United States. https://www.osti.gov/servlets/purl/1364429.
@article{osti_1364429,
title = {Efficient convolutional sparse coding},
author = {Wohlberg, Brendt},
abstractNote = {Computationally efficient algorithms may be applied for fast dictionary learning solving the convolutional sparse coding problem in the Fourier domain. More specifically, efficient convolutional sparse coding may be derived within an alternating direction method of multipliers (ADMM) framework that utilizes fast Fourier transforms (FFT) to solve the main linear system in the frequency domain. Such algorithms may enable a significant reduction in computational cost over conventional approaches by implementing a linear solver for the most critical and computationally expensive component of the conventional iterative algorithm. The theoretical computational cost of the algorithm may be reduced from O(M.sup.3N) to O(MN log N), where N is the dimensionality of the data and M is the number of elements in the dictionary. This significant improvement in efficiency may greatly increase the range of problems that can practically be addressed via convolutional sparse representations.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2017},
month = {6}
}
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