基于Hessian核范数正则化的快速图像复原算法

doi:10.3969/j.issn.0372-2112.2015.10.018

电子学报 ›› 2015, Vol. 43 ›› Issue (10): 2001-2008.DOI: 10.3969/j.issn.0372-2112.2015.10.018

基于Hessian核范数正则化的快速图像复原算法

刘鹏飞¹, 肖亮^1,2

1. 南京理工大学计算机科学与工程学院, 江苏南京 210094;
2. 江苏省光谱成像与智能感知重点实验室, 江苏南京 210094

收稿日期:2014-03-06 修回日期:2014-06-10 出版日期:2015-10-25
- 通讯作者:
- 肖亮
- 作者简介:
- 刘鹏飞 男,1990年出生于安徽安庆,南京理工大学计算机科学与工程学院博士生,研究方向为图像去噪、图像恢复、压缩感知.E-mail:liupengfei199091@163.com
- 基金资助:
- 国家自然科学基金 (No.61171165,No.61302178,No.11431015); 江苏省六大人才高峰项目 (No.2012DZXX-036)

A Fast Algorithm for Image Restoration Based on Hessian Nuclear Norm Regularization

LIU Peng-fei¹, XIAO Liang^1,2

1. School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China;
2. Jiangsu Key Laboratory of Spectral Imaging and Intelligent Sensing, Nanjing, Jiangsu 210094, China

Received:2014-03-06 Revised:2014-06-10 Online:2015-10-25 Published:2015-10-25
- Supported by:
- National Natural Science Foundation of China (No.61171165, No.61302178, No.11431015); Six Talents Peaks in Jiangsu Province (No.2012DZXX-036)

摘要/Abstract

摘要：

利用Hessian核范数进行图像复原是目前较好的高阶正则化方法,但是由于Hessian核范数正则项的高度非线性和不可微性,图像去模糊和去噪过程耦合度高,求解算法的复杂度高.本文利用变量分裂设计了一种具有闭解形式的交替迭代最小化快速图像复原算法,将图像去模糊、去噪分步进行,并给出算法的收敛性证明.实验结果表明,本文方法不仅在峰值信噪比方面优于原有的基于Hessian核范数图像复原的主优化(Majorization-Minimization,MM)方法,而且大大降低了算法的迭代次数和运行时间.

关键词: Hessian核范数, 图像复原, 交替迭代算法

Abstract:

Recently, the Hessian Nuclear norm regularization method has been a preferable higher order regularization scheme for image restoration, but with the Hessian Nuclear norm regularization term been highly non-linear and non-differentiable, image deblurring and denoising processes are highly coupled so that their minimization algorithms are with highly computational complexity.In this paper, we employ variable splitting to design a fast alternating iterative minimization algorithm with closed-form solutions for image restoration, in which we separate image restoration into image deblurring and denoising.Furthermore, we show the convergence of our proposed algorithm.Finally, experimental results demonstrate the effectiveness of the proposed method which consists in not only giving the improved performance in terms of peak signal to noise ratio (PSNR), but also exhibiting a much faster convergence rate than the previous majorization-minimization (MM) method for Hessian Nuclear norm regularization based image restoration.

Key words: Hessian Nuclear norm, image restoration, alternating iterative algorithm

中图分类号:

TN911.73

刘鹏飞, 肖亮. 基于Hessian核范数正则化的快速图像复原算法[J]. 电子学报, 2015, 43(10): 2001-2008.

LIU Peng-fei, XIAO Liang . A Fast Algorithm for Image Restoration Based on Hessian Nuclear Norm Regularization[J]. Acta Electronica Sinica, 2015, 43(10): 2001-2008.

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基于Hessian核范数正则化的快速图像复原算法

A Fast Algorithm for Image Restoration Based on Hessian Nuclear Norm Regularization

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