含Laplace-Gauss型混合噪声图像二阶正则化重建方法

doi:10.19596/j.cnki.1001-246x.7831

计算物理 ›› 2019, Vol. 36 ›› Issue (3): 280-290.DOI: 10.19596/j.cnki.1001-246x.7831

含Laplace-Gauss型混合噪声图像二阶正则化重建方法

孔令海, 孔令波, 许海波, 贾清刚

1. 北京应用物理与计算数学研究所, 北京 100094;
2. 北京交通大学软件工程学院, 北京 100044

收稿日期:2018-01-11 修回日期:2018-07-10 出版日期:2019-05-25 发布日期:2019-05-25
作者简介:Kong Linghai (1970-), male, Shandong Wulian, associate professor, research interests ranges from nonlinear partial differential equations to computational and convex analysis with applications in digital image processing and inverse problems, E-mail:kong_linghai@iapcm.ac.cn
基金资助:
Supported by the National Science Foundation of China (11571003)

A Higher Order Regularization Approach for Object Reconstruction with Mixed Laplace-Gaussian Likelihood

KONG Linghai, KONG Lingbo, XU Haibo, JIA Qinggang

1. Institute of Applied Physics and Computational Mathematics, Beijing 100094, China;
2. School of Software Engineering, Beijing Jiaotong University, Beijing 100044, China

Received:2018-01-11 Revised:2018-07-10 Online:2019-05-25 Published:2019-05-25
Supported by:
Supported by the National Science Foundation of China (11571003)

摘要/Abstract

摘要： 假设观测数据含Laplace-Gauss型混合噪声条件下，提出求解数据重建反问题的一种新型一阶二阶混合正则化模型，阐述该模型在断层重建和流体动力学实验定量诊断中的应用.建模过程采用贝叶斯推断理论和期望极大方法，将空间自适应函数引入经典的增广拉格朗日方法得到模型数值算法.所提出的模型及其算法进行图像复原和客体重建实验.结果表明模型算法的可靠性.

关键词: 客体重建, 自适应软收缩, 四阶偏微分方程, 交替方向增广拉格朗日方法

Abstract: A combined first and second order variational model is proposed for reconstructing images corrupted by mixed Laplace-Gaussian noise. The model is constructed by joint maximum a posteriori estimation and expectation maximization. Numerical algorithm is studied by integrating splitting technique into augmented Lagrangian method with modification, such as introduction of adaptively selective functions for preserving details of original images. An adaptive soft-shrinking formulation is advanced for mixed noise removal, in which an alternating minimization algorithm is established. Numerical experiments show validation in tomography reconstruction and image restoration.

Key words: object reconstruction, adaptive soft-shrinking, fourth-order partial differential equation, ADAL

中图分类号:

O241.8

孔令海, 孔令波, 许海波, 贾清刚. 含Laplace-Gauss型混合噪声图像二阶正则化重建方法[J]. 计算物理, 2019, 36(3): 280-290.

KONG Linghai, KONG Lingbo, XU Haibo, JIA Qinggang. A Higher Order Regularization Approach for Object Reconstruction with Mixed Laplace-Gaussian Likelihood[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 36(3): 280-290.

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含Laplace-Gauss型混合噪声图像二阶正则化重建方法

A Higher Order Regularization Approach for Object Reconstruction with Mixed Laplace-Gaussian Likelihood

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