Inversion formulas and stability estimates of the wave operator on the hyperplane

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:466

Article

Moon, Sunghwan¹ 

[1] Kyungpook Natl Univ, Coll Nat Sci, Dept Math, Daegu 41566, South Korea

关键词: Radon transform;    Photoacoustic;    Tomography;    Spherical means;   

DOI  :  10.1016/j.jmaa.2018.06.006

来源: Elsevier

【 摘 要 】

One of the mathematical problems arising in PhotoAcoustic Tomography (PAT), a novel and promising technology in medical imaging, is to recover the initial function from the solution of the wave equation on a surface, where the detectors of PAT are located. We define the wave operator as the transform assigning to a given function f the solution of the wave equation on the detector surface (where the detectors are located) with the initial function f. Here we study many properties of this wave operator including the inversion formulas and stability estimates assuming that the detector surface is a hyperplane. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free