Learning overcomplete sparsifying transforms for signal processing

Saiprasad Ravishankar, Yoram Bresler

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Adaptive sparse representations have been very popular in numerous applications in recent years. The learning of synthesis sparsifying dictionaries has particularly received much attention, and such adaptive dictionaries have been shown to be useful in applications such as image denoising, and magnetic resonance image reconstruction. In this work, we focus on the alternative sparsifying transform model, for which sparse coding is cheap and exact, and study the learning of tall or overcomplete sparsifying transforms from data. We propose various penalties that control the sparsifying ability, condition number, and incoherence of the learnt transforms. Our alternating algorithm for transform learning converges empirically, and significantly improves the quality of the learnt transform over the iterations. We present examples demonstrating the promising performance of adaptive overcomplete transforms over adaptive overcomplete synthesis dictionaries learnt using K-SVD, in the application of image denoising.

Original languageEnglish (US)
Title of host publication2013 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Proceedings
Pages3088-3092
Number of pages5
DOIs
StatePublished - Oct 18 2013
Event2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Vancouver, BC, Canada
Duration: May 26 2013May 31 2013

Publication series

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

Other

Other2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013
CountryCanada
CityVancouver, BC
Period5/26/135/31/13

Fingerprint

Glossaries
Signal processing
Image denoising
Magnetic resonance
Singular value decomposition
Image reconstruction

Keywords

  • dictionary learning
  • Overcomplete representations
  • Sparse representations
  • Sparsifying transform learning

ASJC Scopus subject areas

  • Signal Processing
  • Software
  • Electrical and Electronic Engineering

Cite this

Ravishankar, S., & Bresler, Y. (2013). Learning overcomplete sparsifying transforms for signal processing. In 2013 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Proceedings (pp. 3088-3092). [6638226] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). https://doi.org/10.1109/ICASSP.2013.6638226

Learning overcomplete sparsifying transforms for signal processing. / Ravishankar, Saiprasad; Bresler, Yoram.

2013 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Proceedings. 2013. p. 3088-3092 6638226 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Ravishankar, S & Bresler, Y 2013, Learning overcomplete sparsifying transforms for signal processing. in 2013 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Proceedings., 6638226, ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, pp. 3088-3092, 2013 38th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013, Vancouver, BC, Canada, 5/26/13. https://doi.org/10.1109/ICASSP.2013.6638226
Ravishankar S, Bresler Y. Learning overcomplete sparsifying transforms for signal processing. In 2013 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Proceedings. 2013. p. 3088-3092. 6638226. (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). https://doi.org/10.1109/ICASSP.2013.6638226
Ravishankar, Saiprasad ; Bresler, Yoram. / Learning overcomplete sparsifying transforms for signal processing. 2013 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013 - Proceedings. 2013. pp. 3088-3092 (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings).
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