AN APPROXIMATE FACTORIZATION METHOD FOR INVERSE ACOUSTIC SCATTERING WITH PHASELESS TOTAL-FIELD DATA.

This paper is concerned with the inverse acoustic scattering problem with phaseless total-field data at a fixed frequency. An approximate factorization method is developed to numerically reconstruct both the location and shape of the unknown scatterer from the phaseless total-field data generated by incident plane waves at a fixed frequency and measured on the circle \partial BR with a sufficiently large radius R. The theoretical analysis of our method is based on the asymptotic property in the operator norm from H1/2(S1) to H 1/2(S1) of the phaseless total-field operator defined in terms of the phaseless total-field data measured on \partial BR with large enough R, where Hs(S1) is a Sobolev space on the unit circle S1 for real number s, together with the factorization of a modified far-field operator. The asymptotic property of the phaseless total-field operator is also established in this paper with the theory of oscillatory integrals. The unknown scatterer can be either an impenetrable obstacle of sound-soft, sound-hard, or impedance type, or an inhomogeneous medium with a compact support, and the proposed inversion algorithm does not need to know the boundary condition of the unknown obstacle in advance. Numerical examples are also carried out to demonstrate the effectiveness of our inversion method. To the best of our knowledge, this is the first attempt to develop a factorization type method for inverse scattering problems with phaseless data. [ABSTRACT FROM AUTHOR]