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Title: Efficient convolutional sparse coding

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:
OSTI Identifier:
1364429
Assignee:
Los Alamos National Security, LLC LANL
Patent Number(s):
9,684,951
Application Number:
14/668,900
Contract Number:
AC52-06NA25396
Resource Relation:
Patent File Date: 2015 Mar 25
Research Org:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Works referenced in this record:

Dictionary Learning with Large Step Gradient Descent for Sparse Representations
book, January 2012
  • Mailhé, Boris; Plumbley, Mark D.; Theis, Fabian
  • Latent Variable Analysis and Signal Separation, p. 231-238
  • DOI: 10.1007/978-3-642-28551-6_29

Alternating Direction Method with Self-Adaptive Penalty Parameters for Monotone Variational Inequalities
journal, August 2000
  • He, B. S.; Yang, H.; Wang, S. L.
  • Journal of Optimization Theory and Applications, Vol. 106, Issue 2, p. 337-356
  • DOI: 10.1023/A:1004603514434