scholarly journals A Coefficient Inverse Problem with a Single Measurement of Phaseless Scattering Data

2019 ◽  
Vol 79 (1) ◽  
pp. 1-27 ◽  
Author(s):  
Michael V. Klibanov ◽  
Dinh-Liem Nguyen ◽  
Loc H. Nguyen
Keyword(s):  
Inverse Problem ◽  
Scattering Data ◽  
Coefficient Inverse Problem ◽  
Single Measurement

scholarly journals A Numerical Method to Solve a Phaseless Coefficient Inverse Problem from a Single Measurement of Experimental Data

2018 ◽  
Vol 11 (4) ◽  
pp. 2339-2367 ◽  
Author(s):  
Michael V. Klibanov ◽  
Nikolay A. Koshev ◽  
Dinh-Liem Nguyen ◽  
Loc H. Nguyen ◽  
Aaron Brettin ◽  
...  
Keyword(s):  
Experimental Data ◽  
Inverse Problem ◽  
Numerical Method ◽  
Coefficient Inverse Problem ◽  
Single Measurement

scholarly journals Convexification for a 1D hyperbolic coefficient inverse problem with single measurement data

2020 ◽  
Vol 14 (5) ◽  
pp. 913-938 ◽  
Author(s):  
Alexey Smirnov ◽  
◽  
Michael Klibanov ◽  
Loc Nguyen
Keyword(s):  
Inverse Problem ◽  
Measurement Data ◽  
Coefficient Inverse Problem ◽  
Single Measurement

scholarly journals A globally convergent numerical method for a 3D coefficient inverse problem with a single measurement of multi-frequency data

2018 ◽  
Vol 12 (2) ◽  
pp. 493-523 ◽  
Author(s):  
Michael V. Klibanov ◽  
◽  
Dinh-Liem Nguyen ◽  
Loc H. Nguyen ◽  
Hui Liu ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Numerical Method ◽  
Frequency Data ◽  
Coefficient Inverse Problem ◽  
Single Measurement ◽  
Globally Convergent

Picosecond scale experimental verification of a globally convergent algorithm for a coefficient inverse problem

2010 ◽  
Vol 26 (4) ◽  
pp. 045003 ◽  
Author(s):  
Michael V Klibanov ◽  
Michael A Fiddy ◽  
Larisa Beilina ◽  
Natee Pantong ◽  
John Schenk
Keyword(s):  
Inverse Problem ◽  
Experimental Verification ◽  
Coefficient Inverse Problem ◽  
Globally Convergent ◽  
Convergent Algorithm

scholarly journals Numerical solution of a coefficient inverse problem with multi-frequency experimental raw data by a globally convergent algorithm

2017 ◽  
Vol 345 ◽  
pp. 17-32 ◽  
Author(s):  
Dinh-Liem Nguyen ◽  
Michael V. Klibanov ◽  
Loc H. Nguyen ◽  
Aleksandr E. Kolesov ◽  
Michael A. Fiddy ◽  
...  
Keyword(s):  
Inverse Problem ◽  
Numerical Solution ◽  
Coefficient Inverse Problem ◽  
Raw Data ◽  
Globally Convergent ◽  
Convergent Algorithm

scholarly journals Near-Field Imaging of Interior Cavities

2015 ◽  
Vol 17 (2) ◽  
pp. 542-563 ◽  
Author(s):  
Peijun Li ◽  
Yuliang Wang
Keyword(s):  
Inverse Problem ◽  
Near Field ◽  
Boundary Value ◽  
Power Series Expansion ◽  
Scattering Data ◽  
Cavity Surface ◽  
Near Field Imaging ◽  
Smooth Perturbation ◽  
Novel Method ◽  
Explicit Relation

AbstractA novel method is developed for solving the inverse problem of reconstructing the shape of an interior cavity. The boundary of the cavity is assumed to be a small and smooth perturbation of a circle. The incident field is generated by a point source inside the cavity. The scattering data is taken on a circle centered at the source. The method requires only a single incident wave at one frequency. Using a transformed field expansion, the original boundary value problem is reduced to a successive sequence of two-point boundary value problems and is solved in a closed form. By dropping higher order terms in the power series expansion, the inverse problem is linearized and an explicit relation is established between the Fourier coefficients of the cavity surface function and the total field. A nonlinear correction algorithm is devised to improve the accuracy of the reconstruction. Numerical results are presented to show the effectiveness of the method and its ability to obtain subwavelength resolution.

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