Sampling type methods for an inverse waveguide problem | Zendy

Peter Monk | Zendy; Virginia Selgás | Zendy

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Sampling type methods for an inverse waveguide problem

Author(s) -

Peter Monk,

Virginia Selgás

Publication year - 2012

Publication title -

inverse problems and imaging

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.755

H-Index - 40

eISSN - 1930-8345

pISSN - 1930-8337

DOI - 10.3934/ipi.2012.6.709

Subject(s) - inverse problem , obstacle , waveguide , reciprocity (cultural anthropology) , point source , computer science , sampling (signal processing) , inverse , acoustics , directional derivative , boundary (topology) , point (geometry) , mathematical analysis , mathematical optimization , mathematics , optics , physics , geometry , telecommunications , psychology , social psychology , detector , law , political science

We consider the problem of locating a penetrable obstacle in an acoustic waveguide from measurements of pressure waves due to point sources inside the waveguide. More precisely, we assume that we are given the scattered field and its normal derivative for any source point and receiver placed on a pair of surfaces known as the source and the measurement surfaces, respectively. A novel feature of this work is that the obstacle is allowed to touch the boundary of the pipe. We first analyze the associated interior transmission problem. Then, we adapt and analyze the Reciprocity Gap Method (RGM) and the Linear Sampling Method (LSM) to deal with the inverse problem. We also study the relationship between these two methods and provide numerical results.

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