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An iterative contractive framework for probe methods: LASSO
Author(s) -
Potthast R. W. E.
Publication year - 2011
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/2011rs004660
Subject(s) - convergence (economics) , near and far field , plane (geometry) , iterative method , lasso (programming language) , point (geometry) , field (mathematics) , function (biology) , mathematics , acoustics , computer science , algorithm , mathematical analysis , physics , optics , geometry , evolutionary biology , world wide web , pure mathematics , economics , biology , economic growth
We present a new iterative approach called Line Adaptation for the Singular Sources Objective (LASSO) to object or shape reconstruction based on the singular sources method (or probe method) for the reconstruction of scatterers from the far‐field pattern of scattered acoustic or electromagnetic waves. The scheme is based on the construction of an indicator function given by the scattered field for incident point sources in its source point from the given far‐field patterns for plane waves. The indicator function is then used to drive the contraction of a surface which surrounds the unknown scatterers. A stopping criterion for those parts of the surfaces that touch the unknown scatterers is formulated. A splitting approach for the contracting surfaces is formulated, such that scatterers consisting of several separate components can be reconstructed. Convergence of the scheme is shown, and its feasibility is demonstrated using a numerical study with several examples.