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
[1]

Jianliang Li, Jiaqing Yang, Bo Zhang. A linear sampling method for inverse acoustic scattering by a locally rough interface. Inverse Problems and Imaging, 2021, 15 (5) : 1247-1267. doi: 10.3934/ipi.2021036

[2]

Fang Zeng. Extended sampling method for interior inverse scattering problems. Inverse Problems and Imaging, 2020, 14 (4) : 719-731. doi: 10.3934/ipi.2020033

[3]

Jingzhi Li, Jun Zou. A direct sampling method for inverse scattering using far-field data. Inverse Problems and Imaging, 2013, 7 (3) : 757-775. doi: 10.3934/ipi.2013.7.757

[4]

Deyue Zhang, Yue Wu, Yinglin Wang, Yukun Guo. A direct imaging method for the exterior and interior inverse scattering problems. Inverse Problems and Imaging, , () : -. doi: 10.3934/ipi.2022025

[5]

Tielei Zhu, Jiaqing Yang. A non-iterative sampling method for inverse elastic wave scattering by rough surfaces. Inverse Problems and Imaging, 2022, 16 (4) : 997-1017. doi: 10.3934/ipi.2022009

[6]

Jun Lai, Ming Li, Peijun Li, Wei Li. A fast direct imaging method for the inverse obstacle scattering problem with nonlinear point scatterers. Inverse Problems and Imaging, 2018, 12 (3) : 635-665. doi: 10.3934/ipi.2018027

[7]

Zhiming Chen, Shaofeng Fang, Guanghui Huang. A direct imaging method for the half-space inverse scattering problem with phaseless data. Inverse Problems and Imaging, 2017, 11 (5) : 901-916. doi: 10.3934/ipi.2017042

[8]

Armin Lechleiter, Marcel Rennoch. Non-linear Tikhonov regularization in Banach spaces for inverse scattering from anisotropic penetrable media. Inverse Problems and Imaging, 2017, 11 (1) : 151-176. doi: 10.3934/ipi.2017008

[9]

Jingzhi Li, Hongyu Liu, Qi Wang. Fast imaging of electromagnetic scatterers by a two-stage multilevel sampling method. Discrete and Continuous Dynamical Systems - S, 2015, 8 (3) : 547-561. doi: 10.3934/dcdss.2015.8.547

[10]

Simopekka Vänskä. Stationary waves method for inverse scattering problems. Inverse Problems and Imaging, 2008, 2 (4) : 577-586. doi: 10.3934/ipi.2008.2.577

[11]

Fang Zeng, Pablo Suarez, Jiguang Sun. A decomposition method for an interior inverse scattering problem. Inverse Problems and Imaging, 2013, 7 (1) : 291-303. doi: 10.3934/ipi.2013.7.291

[12]

Qinghua Wu, Guozheng Yan. The factorization method for a partially coated cavity in inverse scattering. Inverse Problems and Imaging, 2016, 10 (1) : 263-279. doi: 10.3934/ipi.2016.10.263

[13]

Daniela Calvetti, Erkki Somersalo. Microlocal sequential regularization in imaging. Inverse Problems and Imaging, 2007, 1 (1) : 1-11. doi: 10.3934/ipi.2007.1.1

[14]

Laurent Bourgeois, Arnaud Recoquillay. The Linear Sampling Method for Kirchhoff-Love infinite plates. Inverse Problems and Imaging, 2020, 14 (2) : 363-384. doi: 10.3934/ipi.2020016

[15]

Deyue Zhang, Yukun Guo. Some recent developments in the unique determinations in phaseless inverse acoustic scattering theory. Electronic Research Archive, 2021, 29 (2) : 2149-2165. doi: 10.3934/era.2020110

[16]

Alexei Rybkin. On the boundary control approach to inverse spectral and scattering theory for Schrödinger operators. Inverse Problems and Imaging, 2009, 3 (1) : 139-149. doi: 10.3934/ipi.2009.3.139

[17]

Lican Kang, Yanming Lai, Yanyan Liu, Yuan Luo, Jing Zhang. High-dimensional linear regression with hard thresholding regularization: Theory and algorithm. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022034

[18]

Roland Griesmaier. Reciprocity gap music imaging for an inverse scattering problem in two-layered media. Inverse Problems and Imaging, 2009, 3 (3) : 389-403. doi: 10.3934/ipi.2009.3.389

[19]

Teemu Tyni, Valery Serov. Inverse scattering problem for quasi-linear perturbation of the biharmonic operator on the line. Inverse Problems and Imaging, 2019, 13 (1) : 159-175. doi: 10.3934/ipi.2019009

[20]

Markus Harju, Jaakko Kultima, Valery Serov, Teemu Tyni. Two-dimensional inverse scattering for quasi-linear biharmonic operator. Inverse Problems and Imaging, 2021, 15 (5) : 1015-1033. doi: 10.3934/ipi.2021026

2021 Impact Factor: 1.483

Metrics

  • PDF downloads (48)
  • HTML views (0)
  • Cited by (1)

[Back to Top]