On Imaging Models Based On Fractional Order Derivatives Regularizer and Their Iterative Algorithms 基于分数阶导数的图像正则化变分模型与其迭代算法
主 题: On Imaging Models Based On Fractional Order Derivatives Regularizer and Their Iterative Algorithms 基于分数阶导数的图像正则化变分模型与其迭代算法
报告人: Ke Chen (EPSRC Liverpool Centre for Mathematics in Healthcare and Department of Mathematical Sciences, The University of Liverpool, United Kingdom)
时 间: 2017-06-02 11:00-12:00
地 点: 理科1号楼1114
Abstract: In variational imaging and other inverse problem modeling, regularisation plays a major role. In recent years, high order regularizers such as the total generalised variation, the mean curvature and the Gaussian curvature are increasingly studied and applied, and many improved results over the widely-used total variation model are reported.
(1) Here we first introduce the fractional order derivatives and the total fractional-order variation which provides an alternative regularizer and is not yet formally analysed. We demonstrate that existence and uniqueness properties of the new model can be analysed in a fractional BV space, and, equally, the new model performs as well as the high order regularizers (which do not yet have much theory).
(2) In the usual framework, the algorithms of a fractional order model are not fast due to dense matrices involved. Moreover, written in a Bregman framework, the resulting Sylvester equation with Toeplitz coefficients can be solved efficiently by a preconditioned solver. Further ideas based on adaptive integration can also improve the computational efficiency in a dramatic way.
(3) Numerical experiments will be given to illustrate the advantages of the new regulariser for both restoration and regitration problems.
Joint work with Dr J P Zhang (Liverpool/Xiangtan)