Detection, reconstruction, and characterization algorithms from noisy data in multistatic wave imaging
Habib Ammari Josselin Garnier Vincent Jugnon
Discrete & Continuous Dynamical Systems - S 2015, 8(3): 389-417 doi: 10.3934/dcdss.2015.8.389
The detection, localization, and characterization of a collection of targets embedded in a medium is an important problem in multistatic wave imaging. The responses between each pair of source and receiver are collected and assembled in the form of a response matrix, known as the multi-static response matrix. When the data are corrupted by measurement or instrument noise, the structure of the response matrix is studied by using random matrix theory. It is shown how the targets can be efficiently detected, localized and characterized. Both the case of a collection of point reflectors in which the singular vectors have all the same form and the case of small-volume electromagnetic inclusions in which the singular vectors may have different forms depending on their magnetic or dielectric type are addressed.
keywords: random matrices detection and reconstruction algorithms Multistatic wave imaging noisy data Helmholtz equation. measurement noise

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