Location and shape reconstructions of sound-soft obstacles buried in penetrable cylinders

In this paper, we present a method for the solution of a location and shape reconstruction problem related to sound-soft obstacles buried in arbitrarily shaped penetrable cylinders in two dimensions. The direct problem considered here is to obtain the scattered near/far-field in the case of a single time-harmonic acoustic plane wave insonification. The aim of the inverse problem is to find the shape as well as the location of the buried scatterer from the limited/full aperture measurements of the scattered field via Newton iterations. Both for the direct and inverse scattering problems, different potential (layer) approaches are used to derive a system of boundary integral equations. The integral equations are evaluated by using Nystrom and collocation methods. Moreover, in order to obtain a stable solution of the first kind of Fredholm-type integral equations Tikhonov regularization is employed. We test the applicability and the effectiveness of the inversion algorithm also with noisy limited far-field data and obtain satisfactory numerical results as illustrated in the last section.

[1]  R. Kress,et al.  A hybrid method for two-dimensional crack reconstruction , 2005 .

[2]  Eric L. Miller,et al.  Adaptive multiscale reconstruction of buried objects , 2004 .

[3]  Rainer Kress,et al.  Newton’s method for inverse obstacle scattering meets the method of least squares , 2003 .

[4]  Ovidio Mario Bucci,et al.  A novel approach to scatterers localization problem , 2003 .

[5]  Ibrahim Akduman,et al.  Inverse scattering for an impedance cylinder buried in a dielectric cylinder , 2009 .

[6]  Hichem Sahli,et al.  A Nonlinear Iterative Reconstruction and Analysis Approach to Shape-Based Approximate Electromagnetic Tomography , 2008, IEEE Transactions on Geoscience and Remote Sensing.

[7]  Rainer Kress,et al.  A hybrid method for sound-hard obstacle reconstruction , 2007 .

[8]  Rainer Kress,et al.  A second order Newton method for sound soft inverse obstacle scattering , 2009 .

[9]  P. M. van den Berg,et al.  Two‐dimensional location and shape reconstruction , 1994 .

[10]  Pedro Serranho,et al.  A hybrid method for inverse scattering for Sound-soft obstacles in R3 , 2007 .

[11]  T. Isernia,et al.  Improved Sampling Methods for Shape Reconstruction of 3-D Buried Targets , 2008, IEEE Transactions on Geoscience and Remote Sensing.

[12]  Jean-Charles Bolomey,et al.  Electromagnetic Modeling for Microwave Imaging of Cylindrical Buried Inhomogeneities , 1986 .

[13]  Martin Hanke,et al.  A sampling method for detecting buried objects using electromagnetic scattering , 2005 .

[14]  Stéphane Crépey.  Calibration of the local volatility in a trinomial tree using Tikhonov regularization , 2003 .

[15]  Fioralba Cakoni,et al.  Analysis of two linear sampling methods applied to electromagnetic imaging of buried objects , 2006 .

[16]  R. Kleinman,et al.  Microwave imaging-Location and shape reconstruction from multifrequency scattering data , 1997 .

[17]  Ibrahim Akduman,et al.  A generalized ART algorithm for inverse scattering problems related to buried cylindrical bodies , 1995 .

[18]  Ibrahim Akduman,et al.  On the Use of Surface Impedance in the Detection and Location of Buried Objects , 2004 .

[19]  Rainer Kress,et al.  NONLINEAR INTEGRAL EQUATIONS IN INVERSE OBSTACLE SCATTERING , 2006 .

[20]  Dominique Lesselier,et al.  Shape reconstruction of buried obstacles by controlled evolution of a level set: from a min-max formulation to numerical experimentation , 2001 .

[21]  Rainer Kress,et al.  On the numerical solution of a hypersingular integral equation in scattering theory , 1995 .

[22]  W. Chew,et al.  Low-frequency detection of two-dimensional buried objects using high-order extended Born approximations , 2004 .