Sparse Representation Prior and Total Variation-Based Image Deblurring under Impulse Noise

Liyan Ma, Jian Yu, Tieyong Zeng*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

41 Citations (Scopus)
37 Downloads (Pure)


In this paper, we study the image recovery problem where the observed image is simultaneously corrupted by blur and impulse noise. Our proposed patch-based model contains three terms: the sparse representation prior, the total variation regularization, and the data-fidelity term. We are interested in the two-phase approach. The first phase is to identify the possible impulse noise positions; the second phase is to recover the image via the patch-based model using noise position information. An alternating minimization method is then applied to solve the model. This approach works extremely well for image deblurring under salt-and-pepper noise. However, as the detection for random-valued noise is usually unreliable, extra work is then needed. Indeed, to get better recovery results for the latter case, we combine the two separate phases to simultaneously detect the random-valued noise positions and to recover the image. The numerical experiments clearly demonstrate the super performance of the proposed methods.

Original languageEnglish
Pages (from-to)2258-2284
Number of pages27
JournalSIAM Journal on Imaging Sciences
Issue number4
Publication statusPublished - 19 Nov 2013

Scopus Subject Areas

  • Mathematics(all)
  • Applied Mathematics

User-Defined Keywords

  • Dictionary learning
  • Image deblurring
  • Impulse noise
  • Total variation
  • Two-phase method


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