Bayesian inverse problem and optimization with iterative spatial resampling

Iterative Methods for An Inverse Problem

An inverse problem of doubly center matrices is discussed. By translating the constrained problem into unconstrained problem, two iterative methods are proposed. A numerical example illustrate our algorithms.

Optimization with Non-Normal Resampling

AN INVERSE PROBLEM WITH UNKNOWN RADIATION TERM

In this paper, we consider an inverse problem of linear heat equation with nonlinear boundary condition. We identify the temperature and the unknown radiation tern from an overspecified condition on the boundary

Hierarchical Bayesian estimation for MEG inverse problem.

Source current estimation from MEG measurement is an ill-posed problem that requires prior assumptions about brain activity and an efficient estimation algorithm. In this article, we propose a new hierarchical Bayesian method introducing a hierarchical prior that can effectively incorporate both structural and functional MRI data. In our method, the variance of the source current at each source...

Inverse Sturm-Liouville problem with discontinuity conditions

This paper deals with the boundary value problem involving the differential equation begin{equation*}     ell y:=-y''+qy=lambda y,  end{equation*}  subject to the standard boundary conditions along with the following discontinuity  conditions at a point $ain (0,pi)$  begin{equation*}     y(a+0)=a_1 y(a-0),quad y'(a+0)=a_1^{-1}y'(a-0)+a_2 y(a-0), end{equation*} where $q(x),  a_1 , a_2$ are  rea...