学术报告
On Imaging Models Based On Fractional Order Derivatives Regularizer And Their Fast Algorithms - PROF. Ke Chen
报告题目：On Imaging Models Based On Fractional Order Derivatives Regularizer And Their Fast Algorithms
报告人：PROF. Ke Chen
（EPSRC Liverpool Centre for Mathematics in Healthcare and Department of Mathematical Sciences,
The University of Liverpool, United Kingdom）
Web: http://tinyurl.com/EPSRC-LCMH
报告摘要：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.
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).
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.
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 and Xiang-tan).
时间：4月6日（周四）上午9:00-10:00
地点：新教二楼924
