open access

https://doi.org/10.14943/83901

https://hdl.handle.net/2115/69559

The no-response approach and its relation to non-iterative methods for the inverse scattering

英語

2005-10-28

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

751

1-26

The goal of this work is to investigate the relation of the no-response approach to some other non-iterative reconstruction schemes. We will derive several equivalence statements and dependency results. For simplicity we consider the obstacle reconstruction problem from far field data. In particular, we investigate two versions of the no-response test (NRT) for the inverse scattering problem. The first version is the pure NRT, the second combines the NRT with a rangetest element. We show convergence for these two versions without any eigenvalue assumption about the scatterer. Second, we state the natural formulation of the probe method for far field data and reformulate the singular sources method. We show that these statements of the two methods coincide and they form one face of the first version of the no-response test. Third, we prove that the convergence of the linear sampling method implies the convergence of the second version of the no-response test. Precisely, we show that we can use the blowup sequence of the linear sampling method to create the blowup sequence of the second version of the no response test. Fourth, we show that the two versions of the no response method are equivalent with respect to their convergence. Thus, the convergence of the linear sampling method also implies the convergence of the pure no-response test.

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