FRIST - Flipping and rotation invariant sparsifying transform learning and applications

Bihan Wen, Saiprasad Ravishankar, Yoram Bresler

Research output: Contribution to journalArticlepeer-review


Features based on sparse representation, especially using the synthesis dictionary model, have been heavily exploited in signal processing and computer vision. However, synthesis dictionary learning typically involves NP-hard sparse coding and expensive learning steps. Recently, sparsifying transform learning received interest for its cheap computation and its optimal updates in the alternating algorithms. In this work, we develop a methodology for learning flipping and rotation invariant sparsifying transforms, dubbed FRIST, to better represent natural images that contain textures with various geometrical directions. The proposed alternating FRIST learning algorithm involves efficient optimal updates. We provide a convergence guarantee, and demonstrate the empirical convergence behavior of the proposed FRIST learning approach. Preliminary experiments show the promising performance of FRIST learning for sparse image representation, segmentation, denoising, robust inpainting, and compressed sensing-based magnetic resonance image reconstruction.

Original languageEnglish (US)
Article number074007
JournalInverse Problems
Issue number7
StatePublished - Jun 21 2017
Externally publishedYes


  • compressed sensing
  • dictionary learning
  • image denoising
  • inpainting
  • machine learning
  • magnetic resonance imaging
  • sparsifying transform learning

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics


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