Iterative choice of the optimal regularization parameter in TV image deconvolution

3rd International Workshop on New Computational Methods for Inverse Problems

物理学;计算机科学

Sixou, B.^1 ; Toma, A.^1 ; Denis, L.^2 ; Peyrin, F.^1,3

CREATIS, INSA-Lyon, Université de Lyon, 69621 Lyon, France^1

LaHC, CNRS UMR 5516, Université de Saint-Etienne, 42000 Saint-Etienne, France^2

ESRF, Imaging Group, 38043 Grenoble Cedex, France^3

关键词: Alternating direction method of multiplier (ADMM);    Approximate model;    Differentiability;    Exponential models;    Image de convolutions;    Linear inverse problems;    Morozov discrepancy principles;    Optimal regularization;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/464/1/012005/pdf
DOI  :  10.1088/1742-6596/464/1/012005

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

We present an iterative method for choosing the optimal regularization parameter for the linear inverse problem of Total Variation image deconvolution. This approach is based on the Morozov discrepancy principle and on an exponential model function for the data term. The Total Variation image deconvolution is performed with the Alternating Direction Method of Multipliers (ADMM). With a smoothed l2norm, the differentiability of the value of the Lagrangian at the saddle point can be shown and an approximate model function obtained. The choice of the optimal parameter can be refined with a Newton method. The efficiency of the method is demonstrated on a blurred and noisy bone CT cross section.