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Mathematics > Numerical Analysis

arXiv:1812.09545 (math)
[Submitted on 22 Dec 2018 (v1), last revised 1 May 2019 (this version, v2)]

Title:Photoacoustic Tomography with Direction Dependent Data: An Exact Series Reconstruction Approach

Authors:Gerhard Zangerl, Sunghwan Moon, Markus Haltmeier
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Abstract:Photoacoustic image reconstruction often assumes that the restriction of the acoustic pressure on the detection surface is given. However, commonly used detectors often have a certain directivity and frequency dependence, in which case the measured data are more accurately described as a linear combination of the acoustic pressure and its normal derivative on the detection surface. In this paper, we consider the inverse source problem for data that are a combination of an acoustic pressure of the wave equation and its normal derivative For the special case of a spherical detection geometry we derive exact frequency domain reconstruction formulas. We present numerical results showing the robustness and validity of the derived formulas. Moreover, we compare several different combinations of the pressure and its normal derivative showing that used measurement model significantly affects the recovered initial pressure.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:1812.09545 [math.NA]
  (or arXiv:1812.09545v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1812.09545
Related DOI: https://doi.org/10.1088/1361-6420/ab2a30

Submission history

From: Markus Haltmeier [view email]
[v1] Sat, 22 Dec 2018 15:28:13 UTC (207 KB)
[v2] Wed, 1 May 2019 07:00:58 UTC (1,194 KB)
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