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

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 Morozovʹs discrepancy principle is used to find out the regularization parameter.