Entropy- and tikhonov-based regularization techniques applied to the backwards heat equation

• Published in: Computers & mathematics with applications (1987) Vol. 40; no. 8; pp. 1071 - 1084
• Main Authors: Muniz, W.B., Ramos, F.M., de Campos Velho, H.F.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.10.2000
• Subjects: Backwards heat equation; Maximum entropy principle; Tikhonov regularization; Backwards heat equation; Tikhonov regularization; Maximum entropy principle
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/S0898-1221(00)85017-8

The goal of this paper is to analyze the performance of different regularization techniques for an inverse heat conduction problem (IHCP): the estimation of the initial condition. The inverse problem is formulated as a nonlinear constrained optimization problem, and a regularization term is added to the objective function with the help of a regularization parameter. Three classes of regularization methods have been considered: Tikhonov regularization, maximum entropy principle, and truncated singular value decomposition. Concerning the entropíc methodology, two new techniques are introduced and good results were obtained using synthetic data corrupted with noise. The Morozov's discrepancy principle is used to find out the regularization parameter.