REGULARIZATION OF INVERSE ILL-POSED PROBLEMS WITH L2-BV PENALIZERS AND APPLICATIONS TO IMAGE RESTORATION

GISELA L MAZZIERI, RUBEN D SPIES Y KARINA G TEMPERINI

Buenos Aires

Congreso; IV Congreso de Matemática Aplicada, Computacional e Industrial; 2013

Asociación Argentina de Matemática Aplicada, Computacional e industrial y Universidad Nacional de General San martín

Several generalizations of the traditional Tikhonov-Phillips regularization method have been proposed during the last two decades. Many of these generalizations are based upon inducing stability throughout the use of different penalizers which allow the capturing of diverse properties of the exact solution (e.g. edges, discontinuities, borders, etc.). However, in some problems in which it is known that the regularity of the exact solution is heterogeneousor anisotropic, it is reasonable to think that a much better option could be the simultaneous use of two or more penalizers of different nature. Such is the case, for instance, in some image restoration problems in which preservation of edges, borders or discontinuities is an important matter. In this work we present some results on the simultaneous use of penalizers of L2 and of bounded variation (BV) type. For particular cases, existence and uniqueness results will be given. Open problems will be discussed and results to image restoration problems will be presented.