Bayesian K-SVD using fast variational inference

Juan G. Serra, Matteo Testa, Rafael Molina, Aggelos K. Katsaggelos

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

Recent work in signal processing in general and image processing in particular deals with sparse representation related problems. Two such problems are of paramount importance: an overriding need for designing a well-suited overcomplete dictionary containing a redundant set of atoms-i.e., basis signals-and how to find a sparse representation of a given signal with respect to the chosen dictionary. Dictionary learning techniques, among which we find the popular K-singular value decomposition algorithm, tackle these problems by adapting a dictionary to a set of training data. A common drawback of such techniques is the need for parameter-tuning. In order to overcome this limitation, we propose a fullyautomated Bayesian method that considers the uncertainty of the estimates and produces a sparse representation of the data without prior information on the number of non-zeros in each representation vector. We follow a Bayesian approach that uses a three-tiered hierarchical prior to enforce sparsity on the representations and develop an efficient variational inference framework that reduces computational complexity. Furthermore, we describe a greedy approach that speeds up the whole process. Finally, we present experimental results that show superior performance on two different applications with real images: denoising and inpainting.

Original languageEnglish (US)
Article number7875464
Pages (from-to)3344-3359
Number of pages16
JournalIEEE Transactions on Image Processing
Volume26
Issue number7
DOIs
StatePublished - Jul 2017

Keywords

  • Bayesian modeling
  • Denoising
  • Dictionary learning
  • Inpainting
  • Sparse representation
  • Variational inference
  • k-SVD

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design

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