2015/05/07 by Michael V. Klibanov, Klibanov, Michael V., V. G. Romanov +1 · 2 citations
Earth and Planetary Sciences · Engineering · Mathematics · #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Microwave Imaging and Scattering Analysis #Numerical methods in inverse problems #Seismic Imaging and Inversion Techniques #Ultrasonics and Acoustic Wave Propagation
paper · pdf · doi:10.48550/arxiv.1505.01905
openalex publication_date 2015/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is a continuation of two recent publications of the authors about\nreconstruction procedures for 3-d phaseless inverse scattering problems. The\nmain novelty of this paper is that the Born approximation for the case of the\nwave-like equation is not considered. It is shown here that the phaseless\ninverse scattering problem for the 3-d wave-like equation in the frequency\ndomain leads to the well known Inverse Kinematic Problem. Uniqueness theorem\nfollows. Still, since the Inverse Kinematic Problem is very hard to solve, a\nlinearization is applied. More precisely, geodesic lines are replaced with\nstraight lines. As a result, an approximate explicit reconstruction formula is\nobtained via the inverse Radon transform. The second reconstruction method is\nvia solving a problem of the integral geometry using integral equations of the\nAbel type.\n