On level-set type methods for recovering piecewise constant solutions of ill-posed problems

Submitted by Suria Alves (suriaalves@yahoo.com.br) on 2011-08-17T16:37:35Z No. of bitstreams: 1 On Level-Set Type Methods for Recovering Piecewise Constant Solutions of Ill-Posed Problems.pdf: 590806 bytes, checksum: 8890f617dd384f43bab75787a1970053 (MD5)Approved for entry into archive by Barbara Milbrath(barbaramilbrath@yahoo.com.br) on 2011-08-19T02:23:00Z (GMT) No. of bitstreams: 1 On Level-Set Type Methods for Recovering Piecewise Constant Solutions of Ill-Posed Problems.pdf: 590806 bytes, checksum: 8890f617dd384f43bab75787a1970053 (MD5)Made available in DSpace on 2011-08-19T02:23:00Z (GMT). No. of bitstreams: 1 On Level-Set Type Methods for Recovering Piecewise Constant Solutions of Ill-Posed Problems.pdf: 590806 bytes, checksum: 8890f617dd384f43bab75787a1970053 (MD5) Previous issue date: 2009We propose a regularization method for solving ill-posed problems, under the assumption that the solutions are piecewise constant functions with unknown level sets and unknown level values. A level set framework is established for the inverse problem and a Tikhonov regularization approach is proposed. Existence of generalized minimizers for the Tikhonov functional is proven. Moreover, we establish convergence and stability results, characterizing our Tikhonov approach as a regularization method. Based on the necessary conditions of optimality for the Tikhonov functional, a level-set type method is derived and implemented numerically for solving an inverse source problem. This allow us to test the quality of the proposed algorithm