Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

This paper proposes a framelet-based convex optimization model for multiplicative noise and blur removal problem. The main idea is to employ framelet expansion to represent the original image and use the variable decomposition to solve the problem. Because of the nature of multiplicative noise, we decompose the observed data into the original image variable and the noise variable to obtain the resulting model. The original image variable is represented by framelet, and it is determined by using l1-norm in the selection and shrinkage of framelet coefficients. The noise variable is measured by using the mean and the variance of the underlying probability distribution. This framelet setting can be applied to analysis, synthesis, and balanced approaches, and the resulting optimization models are convex, such that they can be solved very efficiently by the alternating direction of a multiplier method. An another contribution of this paper is to propose to select the regularization parameter by using the l1-based L-curve method for these framelet based models. Numerical examples are presented to illustrate the effectiveness of these models and show that the performance of the proposed method is better than that by the existing methods.

Keywords

Numerical models, Image restoration, Optimization, Degradation, Analytical models, Convex functions, Imaging

Publication Date

9-2016

Source Publication Title

IEEE Transactions on Image Processing

Volume

25

Issue

9

Start Page

4222

End Page

4232

Publisher

Institute of Electrical and Electronics Engineers

Peer Reviewed

1

Copyright

© © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

DOI

10.1109/TIP.2016.2583793

Link to Publisher's Edition

https://dx.doi.org/10.1109/TIP.2016.2583793

ISSN (print)

10577149

ISSN (electronic)

19410042

Included in

Mathematics Commons

Share

COinS