Learning sparsifying transforms

Saiprasad Ravishankar, Yoram Bresler

Research output: Contribution to journalArticlepeer-review


The sparsity of signals and images in a certain transform domain or dictionary has been exploited in many applications in signal and image processing. Analytical sparsifying transforms such as Wavelets and DCT have been widely used in compression standards. Recently, synthesis sparsifying dictionaries that are directly adapted to the data have become popular especially in applications such as image denoising, inpainting, and medical image reconstruction. While there has been extensive research on learning synthesis dictionaries and some recent work on learning analysis dictionaries, the idea of learning sparsifying transforms has received no attention. In this work, we propose novel problem formulations for learning sparsifying transforms from data. The proposed alternating minimization algorithms give rise to well-conditioned square transforms. We show the superiority of our approach over analytical sparsifying transforms such as the DCT for signal and image representation. We also show promising performance in signal denoising using the learnt sparsifying transforms. The proposed approach is much faster than previous approaches involving learnt synthesis, or analysis dictionaries.

Original languageEnglish (US)
Article number6339108
Pages (from-to)1072-1086
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number5
StatePublished - 2013


  • Compressed sensing
  • dictionary learning
  • signal denoising
  • sparse representation
  • sparsifying transforms

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing


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