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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 627417, 11 pages
Research Article

Speckle Noise Reduction via Nonconvex High Total Variation Approach

1Department of Health Management, Xi’an Medical University, Xi’an 710021, China
2School of Science, Xidian University, Xi’an 710071, China

Received 9 September 2014; Revised 26 January 2015; Accepted 29 January 2015

Academic Editor: Yaguo Lei

Copyright © 2015 Yulian Wu and Xiangchu Feng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We address the problem of speckle noise removal. The classical total variation is extensively used in this field to solve such problem, but this method suffers from the staircase-like artifacts and the loss of image details. In order to resolve these problems, a nonconvex total generalized variation (TGV) regularization is used to preserve both edges and details of the images. The TGV regularization which is able to remove the staircase effect has strong theoretical guarantee by means of its high order smooth feature. Our method combines the merits of both the TGV method and the nonconvex variational method and avoids their main drawbacks. Furthermore, we develop an efficient algorithm for solving the nonconvex TGV-based optimization problem. We experimentally demonstrate the excellent performance of the technique, both visually and quantitatively.