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Title: 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:
Publication 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 LANL
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. doi:. 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 = {Tue Jun 20 00:00:00 EDT 2017},
month = {Tue Jun 20 00:00:00 EDT 2017}
}

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