欧拉弹性正则化的图像泊松去噪

doi:10.3969/j.issn.0372-2112.2017.01.025

电子学报 ›› 2017, Vol. 45 ›› Issue (1): 181-191.DOI: 10.3969/j.issn.0372-2112.2017.01.025

欧拉弹性正则化的图像泊松去噪

张峥嵘¹, 刘红毅¹, 韦志辉²

1. 南京理工大学理学院, 江苏南京 210094;
2. 南京理工大学计算机科学与技术学院, 江苏南京 210094

收稿日期:2015-07-20 修回日期:2016-03-14 出版日期:2017-01-25
- 通讯作者:
- 刘红毅
- 作者简介:
- 张峥嵘,女,1977年10月出生,江苏淮安人.2015年获南京理工大学计算机科学与工程学院工学博士学位.主要研究方向为图像去噪与恢复,变分法图像处理等.E-mail:zhengrongzhang6@hotmail.com;韦志辉,男,1963年11月出生,江苏淮安人.南京理工大学计算机科学与工程学院教授、博士生导师.主要研究领域为图像建模理论与分析、计算机视觉、遥感图像处理、稀疏表示与压缩感知.E-mail::gswei@mail.njust.edu.cn
- 基金资助:
- 国家自然科学基金 (No.61301215，No.61471199）; 国家自然科学重点基金 (No.11431015）

Image Poisson Denoising Based on Euler's Elastica Regularization

ZHANG Zheng-rong¹, LIU Hong-yi¹, WEI Zhi-hui²

1. School of Science, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China;
2. School of Compute Science and Technology, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China

Received:2015-07-20 Revised:2016-03-14 Online:2017-01-25 Published:2017-01-25
- Supported by:
- National Natural Science Foundation of China (No.61301215, No.61471199); Key Fund of National Natural Science Foundation of China (No.11431015)

摘要/Abstract

摘要：

利用泊松噪声分布与图像灰度值相关这一特性，结合图像的水平集曲线对图像灰度值的刻画能力，在Bayesian-MAP框架下，提出了欧拉弹性正则与泊松似然保真的图像泊松去噪变分正则化模型.利用交替方向乘子法，将原问题转化为几个不同低阶子问题的求解.对于子问题中出现的高阶非线性项，利用滞后扩散不动点迭代进行线性化，从而得到模型的快速迭代求解算法.通过数值模拟实验，证明了当图像受不同强度泊松噪声影响时，所提出的泊松去噪方法都能够有效的抑制泊松噪声，同时具有良好的结构保持性能.

关键词: 泊松去噪, 欧拉弹性, 水平集, 变分正则化

Abstract:

Poisson noise has strong relationship with the gray-values of image,meanwhile the gray-values of image can be represented by level line.In the framework of the Bayesian-MAP,a Poisson denoising variational regularization model is proposed.The Euler's elastica energy is used as a prior regularization term combined with negative-log Poisson likelihood.By using the alternating direction method of multipliers (ADMM),we transform the original high-order optimization problem into several low-order sub-problems.Then the lagged diffusivity fixed point iteration is applied to solve the high-order nonlinear term.For images with strong or weak Poisson noise,experiments show the validity and efficiency of the proposed method both in preserving geometric structure and suppressing noise.

Key words: Poisson denoising, Euler's elastica, level line, variational regularization

中图分类号:

TP391

张峥嵘, 刘红毅, 韦志辉. 欧拉弹性正则化的图像泊松去噪[J]. 电子学报, 2017, 45(1): 181-191.

ZHANG Zheng-rong, LIU Hong-yi, WEI Zhi-hui . Image Poisson Denoising Based on Euler's Elastica Regularization[J]. Acta Electronica Sinica, 2017, 45(1): 181-191.

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欧拉弹性正则化的图像泊松去噪

Image Poisson Denoising Based on Euler's Elastica Regularization

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