Photo-acoustic inversion in convex domains | Zendy

Frank Natterer | Zendy

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Photo-acoustic inversion in convex domains

Author(s) -

Frank Natterer

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.2012.6.315

Subject(s) - modulo , inversion (geology) , regular polygon , smoothing , operator (biology) , surface (topology) , convex function , mathematics , mathematical analysis , function (biology) , geometry , combinatorics , geology , paleontology , biochemistry , statistics , chemistry , repressor , structural basin , evolutionary biology , biology , transcription factor , gene

In photo-acoustics one has to reconstruct a function from its averages over spheres around points on the measurement surface. For special surfaces inversion formulas are known. In this paper we derive a formula for surfaces that bound smooth convex domains. It reconstructs the function modulo a smoothing integral operator. For special surfaces the integral operator vanishes, providing exact reconstruction.

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