# American Institute of Mathematical Sciences

May  2009, 3(2): 231-241. doi: 10.3934/ipi.2009.3.231

## Imaging of unknown targets inside inhomogeneous backgrounds by means of qualitative inverse scattering

 1 Dipartimento di Ingegneria Biofisica ed Elettronica, Università di Genova, via Opera Pia 11a, Genova, I-16145, Italy 2 Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, I-16146 Genova, Italy 3 Dipartimento di Ingegneria Biofisica ed Elettronica, Università di Genova, via Opera Pia 11a, I-16145 Genova, Italy, Italy 4 Dipartimento di Informatica, Università di Genova, Strada le Grazie 15, I-16146 Verona

Received  November 2008 Revised  March 2009 Published  May 2009

In this paper a new formulation of the Linear Sampling Method, called the no-Sampling Linear Sampling Method, is applied to the imaging and detection of unknown scatterers located inside an inhomogeneous background. Namely, by following a previous work by Colton and Monk, a modified far--field equation is used, which allows one to use line current sources and nearfield measurements. The Green's function of the inhomogeneous background is numerically computed and used as the right hand side of the modified farfield equation. The proposed method is then applied to two different scenarios: the detection of breast tumors and the imaging of cracks inside a dielectric slab. A numerical analysis of the method capabilities is performed when the model parameters are not exactly known.
Citation: Giovanni Bozza, Massimo Brignone, Matteo Pastorino, Andrea Randazzo, Michele Piana. Imaging of unknown targets inside inhomogeneous backgrounds by means of qualitative inverse scattering. Inverse Problems and Imaging, 2009, 3 (2) : 231-241. doi: 10.3934/ipi.2009.3.231
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