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Title: Fredholm integral equation for shape reconstruction of an underwater object using backscattered ramp response signatures
Authors: Li, W.
Liu, G.R. 
Varadan, V.K.
Issue Date: Sep-2004
Citation: Li, W., Liu, G.R., Varadan, V.K. (2004-09). Fredholm integral equation for shape reconstruction of an underwater object using backscattered ramp response signatures. Journal of the Acoustical Society of America 116 (3) : 1436-1445. ScholarBank@NUS Repository.
Abstract: Inverse scattering problems for identifying underwater objects are of importance for all kinds of applications in seas that occupy more than two-thirds of the surface of the earth. The physical optics approximation has been applied to the acoustic scattering integral representation, yielding an inverse scattering equation which relates the profile function of a submerged object to the Fourier transform of the complex backscattered acoustic field. This technique is the so-called ramp response technique and usually requires the full scattering information for all frequencies to obtain accurate profile function of an object. In order to retrieve the shape information of an object from the band-limited backscattered frequency data, a Fredholm integral equation is formulated in this paper for calculating the ramp response of the submerged object. This Fredholm integral equation is for the unknown ramp response of an object in terms of the known incomplete scattering information. The kernel of this integral equation is the inverse Fourier transform of the known characteristic function of the scattering information aperture. In order to simulate the real experiment environment, a computer-generated Gauss noise is added directly to the simulated impulse response. This noise-contaminated impulse response is then used for the inverse identification of the underwater object. It is found that adding noise would lead to the ill-posedness of this inverse scattering problem. To deal with the ill-posedness, the regularization method by filtering is employed. Numerical examples have confirmed that the method presented in this paper can successfully reconstruct the shape of an underwater object using an incomplete set of backscattered frequency data with or without noise contamination. Meanwhile, the effect of bandwidth to the ramp response is also discussed in the numerical examples. © 2004 Acoustical Society of America.
Source Title: Journal of the Acoustical Society of America
ISSN: 00014966
DOI: 10.1121/1.1776190
Appears in Collections:Staff Publications

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