Commun. Comput. Phys.,
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Volume 4.


An Energy Regularization Method for the Backward Diffusion Problem and its Applications to Image Deblurring

Houde Han 1, Ming Yan 1*, Chunlin Wu 1

1 Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China.

Received 5 June 2007; Accepted (in revised version) 5 November 2007
Available online 27 February 2008

Abstract

For the backward diffusion equation, a stable discrete energy regularization algorithm is proposed. Existence and uniqueness of the numerical solution are given. Moreover, the error between the solution of the given backward diffusion equation and the numerical solution via the regularization method can be estimated. Some numerical experiments illustrate the efficiency of the method, and its application in image deblurring.

AMS subject classifications: 65M12, 65M30, 86A22, 94A08

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Key words: Energy regularization method, inverse problem, heat equation, backward diffusion equation, image deblurring, error estimate, ill-posed, well-posed.

*Corresponding author.
Email: hhan@math.tsinghua.edu.cn (H. D. Han), yanmingy@mail.ustc. edu.cn (M. Yan), wucl@ustc.edu.cn (C. L. Wu)
 

The Global Science Journal