Ill-posed problems and the methods of their solution

The formal solution of the ill-posed inverse problem could result in unstable, unrealistic models. The regularization theory provides a guidance how one can overcome this difficulty. The foundations of the regularization theory were developed in numerous publications by Andrei N. Tikhonov, which were reprinted in 1999 as a special book, published by Moscow State University (Tikhonov, 1999). In this Chapter, I will present a short overview of the basic principles of the Tikhonov regularization theory, following his original monograph (Tikhonov and Arsenin, 1977). 

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