Topological derivative-based technique for imaging thin inhomogeneities with few incident directions
Provides theoretical justification and optimal configuration guidance for topological derivative imaging, reducing required incident directions for practitioners in non-destructive testing or medical imaging.
The paper analyzes the mathematical structure of topological derivative-based imaging for thin inhomogeneities, showing that only a few incident directions suffice and identifying optimal configurations, supported by numerical simulations.
Many non-iterative imaging algorithms require a large number of incident directions. Topological derivative-based imaging techniques can alleviate this problem, but lacks a theoretical background and a definite means of selecting the optimal incident directions. In this paper, we rigorously analyze the mathematical structure of a topological derivative imaging function, confirm why a small number of incident directions is sufficient, and explore the optimal configuration of these directions. To this end, we represent the topological derivative based imaging function as an infinite series of Bessel functions of integer order of the first kind. Our analysis is supported by the results of numerical simulations.