The point source method for inverse scattering in the time domain

• Published in: Mathematical methods in the applied sciences Vol. 29; no. 13; pp. 1501 - 1521
• Main Authors: Russell Luke, D., Potthast, Roland
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 10.09.2006; Wiley; Teubner
• Subjects: Applied sciences; Artificial intelligence; Classical and quantum physics: mechanics and fields; Computer science; control theory; systems; Exact sciences and technology; Fourier analysis; General theory of scattering; image reconstruction; inverse problems; Mathematical analysis; Mathematics; Pattern recognition. Digital image processing. Computational geometry; Physics; scattering theory; Sciences and techniques of general use; time-domain scattering; Fourier transformation; Applied mathematics; Inverse scattering method; inverse problems; Numerical method; Time-domain scattering; Algorithm; Image reconstruction; Inverse problem; Point source; Scattering theory
• ISSN: 0170-4214; 1099-1476; 1099-1476
• DOI: 10.1002/mma.738

Many recent inverse scattering techniques have been designed for single frequency scattered fields in the frequency domain. In practice, however, the data is collected in the time domain. Frequency domain inverse scattering algorithms obviously apply to time‐harmonic scattering, or nearly time‐harmonic scattering, through application of the Fourier transform. Fourier transform techniques can also be applied to non‐time‐harmonic scattering from pulses. Our goal here is twofold: first, to establish conditions on the time‐dependent waves that provide a correspondence between time domain and frequency domain inverse scattering via Fourier transforms without recourse to the conventional limiting amplitude principle; secondly, we apply the analysis in the first part of this work toward the extension of a particular scattering technique, namely the point source method, to scattering from the requisite pulses. Numerical examples illustrate the method and suggest that reconstructions from admissible pulses deliver superior reconstructions compared to straight averaging of multi‐frequency data. Copyright © 2006 John Wiley & Sons, Ltd.