Abstract

We investigate regularization methods for solving the problem of crack detection in bounded planar domains from electrical measurements on the boundary. Based on the multiple level-set approach introduced in alvarez et al (2009 J. Comput. Phys. 228 5710-21) and on the regularization strategy devised in De Cezaro et al (2009 Inverse Problems 25 035004), we propose a Tikhonov type method for stabilizing the inverse problem. Convergence and stability results for this Tikhonov method are proven. An iterative method of (multiple) level-set type is derived from the optimality conditions for the Tikhonov functional, and a relation between this method and the iterated Tikhonov method is established. The proposed level-set method is tested on the same benchmark problem considered in alvarez et al (2009 J. Comput. Phys. 228 5710-21). The numerical experiments demonstrate its ability to identify cracks in different scenarios with high accuracy even in the presence of noise.