A framelet algorithm for de-blurring images corrupted by multiplicative noise

Jian Lu, Zeping Yang, Lixin Shen, Zhaosong Lu, Hanmei Yang, Chen Xu

Research output: Contribution to journalArticle

5 Scopus citations


This paper considers a variational model for restoring images from blurry and speckled observations. This model utilizes the favorable properties of framelet regularization (e.g., the sparsity and multiresolution properties of the framelet) that are well suited for speckle noise reduction. For solving the model, we first propose an approximation model that is motivated by the well-known variable-splitting and penalty techniques in optimization. We then develop an alternating minimization algorithm to solve the approximation model. We also show that the sequence generated by the algorithm converges to the solution of the proposed model. The numerical results on simulated data and real utrasound images demonstrate that our approach outperforms several state-of-the-art algorithms.

Original languageEnglish (US)
Pages (from-to)51-61
Number of pages11
JournalApplied Mathematical Modelling
StatePublished - Oct 2018
Externally publishedYes


  • Framelet
  • Multiplicative noise
  • Restoring blurred images
  • Ultrasound images

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