Doubly sparse transform learning with convergence guarantees

Saiprasad Ravishankar, Yoram Bresler

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

Abstract

The sparsity of natural signals in transform domains such as the DCT has been heavily exploited in various applications. Recently, we introduced the idea of learning sparsifying transforms from data, and demonstrated the usefulness of learnt transforms in image representation, and denoising. However, the learning formulations therein were non-convex, and the algorithms lacked strong convergence properties. In this work, we propose a novel convex formulation for square sparsifying transform learning. We also enforce a doubly sparse structure on the transform, which makes its learning, storage, and implementation efficient. Our algorithm is guaranteed to converge to a global optimum, and moreover converges quickly. We also introduce a non-convex variant of the convex formulation, for which the algorithm is locally convergent. We show the superior promise of our learnt transforms as compared to analytical sparsifying transforms such as the DCT for image representation.

Original languageEnglish (US)
Title of host publication2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5262-5266
Number of pages5
ISBN (Print)9781479928927
DOIs
StatePublished - Jan 1 2014
Event2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014 - Florence, Italy
Duration: May 4 2014May 9 2014

Publication series

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

Other

Other2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014
CountryItaly
CityFlorence
Period5/4/145/9/14

Keywords

  • Convex learning
  • Sparse representations

ASJC Scopus subject areas

  • Signal Processing
  • Software
  • Electrical and Electronic Engineering

Cite this

Ravishankar, S., & Bresler, Y. (2014). Doubly sparse transform learning with convergence guarantees. In 2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014 (pp. 5262-5266). [6854607] (ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICASSP.2014.6854607