2015
DOI: 10.1515/jiip-2015-0083
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Fast Toeplitz linear system inversion for solving two-dimensional acoustic inverse problem

Abstract: The coefficient inverse problem for the acoustic equation is considered. We propose the method for reconstructing the density based on the

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Cited by 34 publications
(26 citation statements)
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“…Therefore, the vector function F (y ) is quadratic with respect to the functions y n (x) . In addition, (30) and (32) imply that y (x) satisfies the following boundary conditions:…”
Section: A System Of Coupled Quasilinear Ordinary Differential Equationsmentioning
confidence: 99%
“…Therefore, the vector function F (y ) is quadratic with respect to the functions y n (x) . In addition, (30) and (32) imply that y (x) satisfies the following boundary conditions:…”
Section: A System Of Coupled Quasilinear Ordinary Differential Equationsmentioning
confidence: 99%
“…Another quite interesting application is in inverse scattering of electromagnetic waves, in which case c −2 (y) = ε r (y), where ε r (y) is the spatially distributed dielectric constant. Using the data, which were experimentally collected by the US Army Research Laboratory, it was demonstrated in [14,24,32] that the 1D mathematical model, which is based on equation (1.5), can be quite effectively used to image in the standoff mode dielectric constants of targets, which mimic explosives, such as, e.g. antipersonnel land mines and improvised explosive devices.…”
mentioning
confidence: 99%
“…antipersonnel land mines and improvised explosive devices. In fact, the original data in [14,24,32] were collected in the time domain. However, the mathematical apparatus of these references works only either with the Laplace transform [14,32] or with the Fourier transform [24] with respect to t of equation (1.5).…”
mentioning
confidence: 99%
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“…In all these four publications truncated Fourier series were used to develop new numerical methods and to test them numerically. Although convergence estimates at N → ∞ were not provided in [6,8,9,10], numerical results are quite accurate ones.…”
Section: Problem ( 53) ( 54) In the Semidiscrete Formmentioning
confidence: 95%