Blind compressed sensing using sparsifying transforms

Saiprasad Ravishankar, Yoram Bresler

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

Abstract

Compressed sensing exploits the sparsity of images or image patches in a transform domain or synthesis dictionary to reconstruct images from undersampled measurements. In this work, we focus on blind compressed sensing, where the underlying sparsifying transform is a priori unknown, and propose a framework to simultaneously reconstruct both the image and the transform from highly undersampled measurements. The proposed block coordinate descent type algorithm involves efficient updates. Importantly, we prove that although the proposed formulation is highly nonconvex, our algorithm converges to the set of critical points of the objective defining the formulation. We illustrate the promise of the proposed framework for magnetic resonance image reconstruction from highly undersampled k-space measurements. As compared to previous methods involving fixed sparsifying transforms, or adaptive synthesis dictionaries, our approach is much faster, while also providing promising image reconstructions.

Original languageEnglish (US)
Title of host publication2015 International Conference on Sampling Theory and Applications, SampTA 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages513-517
Number of pages5
ISBN (Electronic)9781467373531
DOIs
StatePublished - Jul 2 2015
Event11th International Conference on Sampling Theory and Applications, SampTA 2015 - Washington, United States
Duration: May 25 2015May 29 2015

Publication series

Name2015 International Conference on Sampling Theory and Applications, SampTA 2015

Other

Other11th International Conference on Sampling Theory and Applications, SampTA 2015
CountryUnited States
CityWashington
Period5/25/155/29/15

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Signal Processing
  • Statistics and Probability

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    Ravishankar, S., & Bresler, Y. (2015). Blind compressed sensing using sparsifying transforms. In 2015 International Conference on Sampling Theory and Applications, SampTA 2015 (pp. 513-517). [7148944] (2015 International Conference on Sampling Theory and Applications, SampTA 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SAMPTA.2015.7148944