|Abstract:|| The problem of determining the location, size and shape of objects embedded in a medium has attracted a lot of attention in recent years. The problem is of paramount interest in a variety of fields, including medical imaging, non-destructive testing of materials, and natural resources exploration. A number of numerical methods have been proposed to solve inverse obstacle problems. The most commonly used iterative methods have the disadvantage of requiring an accurate initial guess. Notwithstanding, in practical situations it is not realistic to assume that the number of objects and their approximate location or size are known beforehand. On the other hand, it is usual to assume that several incident waves are generated with a full aperture angle distribution, and that the receivers are located around the objects. However, in many applications these assumptions are again not realistic.
In this talk we present numerical methods based on topological derivative computations. The idea behind the method is to generate an indicator function able to classify each point of the region of interest as either belonging to the background medium or to an object, without any a priori assumption. Numerical tests illustrating the viability of the techniques in different situations including the simultaneous reconstruction of objects of different sizes, and fairly demanding measurement configurations with a very reduced number of emitters and receivers located in a small region will be shown.
Referenti: Elena Beretta e Marco Verani