A Backward Heat Conduction Problem With Application To Image Processing

In this paper, we consider a fractional backward heat conduction problem(BHCP) which is associated with debluring problem in image processing. For thisill-posed problem, we first propose an optimal filtering regularization method tosolve the problem with noisy data and obtain the stability error estimation, andthen we propose two quasi-boundary regularization methods to solve the problemwith noisy data and obtain the optimal stability error estimation. In addition, wealso give some numerical examples in order to show that our proposed optimal filter-ing regularization method and quasi-boundary regularization methods are efectiveand feasible.This paper is divided into three sections:in Sencton1, we will briefly introduce the mathematical model related to thistopic;in Sencton2, we will introduce the optimal filtering regularization method andprove the error esimate. Numerical experiment is given for illustrating the feasibilityof the optimal method, this part has been published in the Journal of ApplicableAnalysis;in Sencton3, we will devise two quasi-boundary regularization methods for theproblem, and compare with the classical Tikhonov method.