Linear sampling method for acoustic inverse scattering in breast microcalcification detection

2006 ◽  
Vol 120 (5) ◽  
pp. 3025-3025 ◽  
Author(s):  
Matthew A. Lewis ◽  
Peiying Liu ◽  
Edmond Richer ◽  
Peter P. Antich ◽  
Stuart G. Johnson
Keyword(s):  
Inverse Scattering ◽  
Sampling Method ◽  
Linear Sampling Method ◽  
Breast Microcalcification ◽  
Microcalcification Detection ◽  
Acoustic Inverse Scattering ◽  
Linear Sampling

The Linear Sampling Method as a Way to Quantitative Inverse Scattering

2012 ◽  
Vol 60 (4) ◽  
pp. 1844-1853 ◽  
Author(s):  
Lorenzo Crocco ◽  
Ilaria Catapano ◽  
Loreto Di Donato ◽  
Tommaso Isernia
Keyword(s):  
Inverse Scattering ◽  
Sampling Method ◽  
Linear Sampling Method ◽  
Linear Sampling

scholarly journals On the Mathematical Basis of the Linear Sampling Method

2003 ◽  
Vol 10 (3) ◽  
pp. 411-425
Author(s):  
Fioralba Cakoni ◽  
David Colton
Keyword(s):  
Inverse Scattering ◽  
Electromagnetic Waves ◽  
Sampling Method ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Linear Integral Equation ◽  
Mathematical Basis ◽  
Linear Sampling Method ◽  
Mathematical Justification ◽  
Linear Sampling

Abstract The linear sampling method is an algorithm for solving the inverse scattering problem for acoustic and electromagnetic waves. The method is based on showing that a linear integral equation of first kind has a solution that becomes unbounded as a parameter 𝑧 approaches the boundary of the scatterer 𝐷 from inside 𝐷. However, except for the case of the transmission problem, the case where z is in the exterior of 𝐷 is unresolved. Since for the inverse scattering problem 𝐷 is unknown, this step is crucial for the mathematical justification of the linear sampling method. In this paper we give a mathematical justification of the linear sampling method for arbitrary 𝑧 by using the theory of integral equations of first kind with singular kernels.

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