On Level-Set Type Methods for Recovering Piecewise Constant Solutions of Ill-Posed Problems

We 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.

• Type: Conference
• Year: 2009
• Where: SCALESPACE
• Authors: Adriano DeCezaro, Antonio Leitão, Xue-Cheng Tai
• Keywords: Computer Vision, Level Set, Regularization Method, SCALESPACE 2009, Unknown Level