We deal with a boundary detection problem arising in nondestructive testing of materials.
The problem consists in recovering an unknown portion of the boundary, where a Robin
condition is satisfied, with the use of a Cauchy data pair collected on the accessible part
of the boundary. We combine a linearization argument with a Tikhonov regularization
approach for the local reconstruction of the unknown defect. Moreover, we discuss the regularization
parameter choice by means of the so called balancing principle and we present
some numerical tests that show the efficiency of our method.
