Data-Driven Learning of a Union of Sparsifying Transforms Model for Blind Compressed Sensing

Saiprasad Ravishankar, Yoram Bresler

Research output: Contribution to journalArticlepeer-review


Compressed sensing is a powerful tool in applications such as magnetic resonance imaging (MRI). It enables accurate recovery of images from highly undersampled measurements by exploiting the sparsity of the images or image patches in a transform domain or dictionary. In this work, we focus on blind compressed sensing (BCS), where the underlying sparse signal model is a priori unknown, and propose a framework to simultaneously reconstruct the underlying image as well as the unknown model from highly undersampled measurements. Specifically, our model is that the patches of the underlying image(s) are approximately sparse in a transform domain. We also extend this model to a union of transforms model that better captures the diversity of features in natural images. The proposed block coordinate descent type algorithms for BCS are highly efficient, and are guaranteed to converge to at least the partial global and partial local minimizers of the highly nonconvex BCS problems. Our numerical experiments show that the proposed framework usually leads to better quality of image reconstructions in MRI compared to several recent image reconstruction methods. Importantly, the learning of a union of sparsifying transforms leads to better image reconstructions than a single adaptive transform.

Original languageEnglish (US)
Article number7468471
Pages (from-to)294-309
Number of pages16
JournalIEEE Transactions on Computational Imaging
Issue number3
StatePublished - Sep 2016


  • Compressed sensing
  • dictionary learning
  • inverse problems
  • machine learning
  • magnetic resonance imaging
  • medical imaging
  • sparse representations
  • sparsifying transforms

ASJC Scopus subject areas

  • Signal Processing
  • Computer Science Applications
  • Computational Mathematics


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