Shape reconstruction from PO multifrequency scattered fields via the singular value decomposition approach

Abstract

This paper deals with the problem of determining the shape of unknown perfectly conducting infinitely long cylinders, starting from the knowledge of the scattered electric far field under the incidence of plane waves with a fixed angle of incidence and varying frequency. The problem is formulated as a nonlinear inverse one by searching for a compact support distribution accounting for the objects contour. The nonlinear unknown to data mapping is then linearized by means of the Kirchhoff approximation, which reduces it into a Fourier transform relationship. Then, the Fourier transform inversion from incomplete data is dealt with by means of the singular value decomposition (SVD) approach and the features of the reconstructable unknowns are investigated. Finally, numerical results confirm the performed analysis.