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

The goal of this paper is to analyze the performance of different regulariz ation techniques for an inverse heat conduction problem (IHCP): the estimat ion of the initial condition. The inverse problem is formulated as a nonlin ear 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 regulariza tion, maximum entropy principle, and truncated singular value decomposition . Concerning the entropic methodology, two new techniques are introduced an d good results were obtained using synthetic data corrupted with noise. The Morozov's discrepancy principle is used to find out the regularization par ameter. (C) 2000 Elsevier Science Ltd. All rights reserved.