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

LIU Peng-fei; XIAO Liang

doi:10.3969/j.issn.0372-2112.2015.10.018

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

更新时间：2025-07-16

- A Fast Algorithm for Image Restoration Based on Hessian Nuclear Norm Regularization
- Acta Electronica Sinica Vol. 43, Issue 10, Pages: 2001-2008(2015)
- 作者机构：
  
  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
  3. 南京理工大学计算机科学与工程学院,江苏,南京,210094
  4. 江苏省光谱成像与智能感知重点实验室,江苏,南京,210094
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61171165, No.61302178, No.11431015);Six Talents Peaks in Jiangsu Province (No.2012DZXX-036)
- DOI：10.3969/j.issn.0372-2112.2015.10.018
  CLC： TN911.73
- Published：2015
- 稿件说明：
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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.
DOI：

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. DOI： 10.3969/j.issn.0372-2112.2015.10.018.

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.

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.

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