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 journalArticlepeer-review

12 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

Bibliographical note

Funding Information:
The authors would like to thank Dr. Zhengmeng Jin for providing the source code of JY method. This work was supported in part by the National Natural Science Foundation of China under grants 61373087 , 11201312 , 61472257, by China Scholarship Council, by the Natural Science Foundation of Guangdong , China under grants 2015A030313550 , 2015A030313557 , by the Foundation for Distinguished Young Teachers in Higher Education of Guangdong, China under grant Yq2013144, by the Specialized Research Fund for the Doctoral Program of Higher Education of China under grant 20134408110001, by the HD Video R & D Platform for Intelligent Analysis and Processing in Guangdong Engineering Technology Research Centre of Colleges and Universities (No. GCZX-A1409), by the Shenzhen Key Laboratory of Media Security, and by the US National Science Foundation under Grant DMS-1522332.

Publisher Copyright:
© 2018 Elsevier Inc.


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


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