利用平衡方法的非凸图像修复

doi:10.3969/j.issn.1001-2400.2014.05.024

J4 ›› 2014, Vol. 41 ›› Issue (5): 141-147.doi: 10.3969/j.issn.1001-2400.2014.05.024

利用平衡方法的非凸图像修复

吴玉莲^1,2;冯象初¹

(1. 西安电子科技大学数学与统计学院，陕西西安 710071；
2. 西安医学院公共课部，陕西西安 710021)

收稿日期:2013-05-16 出版日期:2014-10-20 发布日期:2014-11-27
通讯作者: 吴玉莲
作者简介:吴玉莲(1978-)，女，西安电子科技大学博士研究生，E-mail:wyl_wp711@163.com．
基金资助:
国家自然科学基金资助项目(61271294)

Nonconvex image inpainting via balanced regularization approach

WU Yulian^1,2;FENG Xiangchu¹

(1. School of Mathematics and Statistics, Xidian Univ., Xi'an 710071, China;
2. Common Course Department, Xi'an Medical College, Xi'an 710021, China)

Received:2013-05-16 Online:2014-10-20 Published:2014-11-27
Contact: WU Yulian

摘要/Abstract

摘要：

自然图像通常可以看成由两部分构成：卡通部分和纹理部分，这两部分在一些紧框架下，比如曲线波、局部余弦变换、样条小波等都有稀疏表示．该文研究在两个可分离紧框架下的图像修复问题．与大部分算法普遍采用基于分析的或者合成的稀疏先验的不同之处在于：文中采用基于平衡的方法，且对稀疏系数使以非凸限制；最后给出了迭代算法．数值实验表明了建议的非凸图像修复方法比普通的l₁凸方法和经典的变分TV方法有更好的修复效果．

关键词: 图像修复, 卡通纹理, 非凸, 紧框架

Abstract:

Real images usually have two layers, namely, cartoons and textures, both of these layers have sparse approximations under some tight frame systems such as curvelet, local DCTs, and B-spline wavelet. In this paper, we solve the image inpainting problem by using two separate tight frame systems which can sparsely represent the two parts of the image. Different from existing schemes in the literature which are either analysis-based or synthesis-based sparsity priors, our minimization formulation applies the nonconvex sparsity prior via the balanced approach. We also derive iterative algorithms for finding their solutions. Numerical simulation examples are given to demonstrate that our proposed nonconvex method achieves significant improvements over the classical l₁ sparse method and the variation TV method in image inpainting.

Key words: image inpainting, cartoons and textures, nonconvex, tight frame systems

吴玉莲;冯象初. 利用平衡方法的非凸图像修复[J]. J4, 2014, 41(5): 141-147.

WU Yulian;FENG Xiangchu. Nonconvex image inpainting via balanced regularization approach[J]. J4, 2014, 41(5): 141-147.

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利用平衡方法的非凸图像修复

Nonconvex image inpainting via balanced regularization approach

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