Fast convolutional sparse coding with separable filters

Gustavo Silva, Jorge Quesada, Paul Rodríguez, Brendt Wohlberg

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

13 Scopus citations

Abstract

Convolutional sparse representations (CSR) of images are receiving increasing attention as an alternative to the usual independent patch-wise application of standard sparse representations. For CSR the dictionary is a filter bank of non-separable 2D filters, and the representation itself can be viewed as the synthesis dual of the analysis representation provided by a single level of a convolutional neural network (CNN). The current state-of-the-art convolutional sparse coding (CSC) algorithms achieve their computational efficiency by applying the convolutions in the frequency domain. It has been shown that any given 2D non-separable filter bank can be approximated as a linear combination of a relatively small number of separable filters. This approximation has been exploited for computationally efficient CNN implementations, but has thus far not been considered for convolutional sparse coding. In this paper we propose a computationally efficient algorithm, that apply the convolution in the spatial domain, to solve the CSC problem when the corresponding dictionary filters are separable. Our algorithm, based on the ISTA framework, use a two-term penalty function to attain competitive results when compared to the state-of-the-art methods in terms of computational performance, sparsity and reconstruction quality.

Original languageEnglish
Title of host publication2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages6035-6039
Number of pages5
ISBN (Electronic)9781509041176
DOIs
StatePublished - 16 Jun 2017
Event2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017 - New Orleans, United States
Duration: 5 Mar 20179 Mar 2017

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Conference

Conference2017 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2017
Country/TerritoryUnited States
CityNew Orleans
Period5/03/179/03/17

Keywords

  • Convolutional Sparse Coding
  • Convolutional Sparse Representation
  • Separable Filters

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