2006/10/04 by Markus Haltmeier, Haltmeier, M., T C FIDLER +1
Engineering · Medicine · #35L05 #44A12 #65R32. #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA) #Photoacoustic and Ultrasonic Imaging #Thermography and Photoacoustic Techniques #Ultrasound Imaging and Elastography
paper · pdf · doi:10.48550/arxiv.math/0610155
openalex publication_date 2006/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Thermoacoustic computed tomography (thermoacoustic CT) has the potential to become a mayor non-invasive medical imaging method. In this paper we derive a general mathematical framework of a novel measuring setup introduced in [P. Burgholzer, C. Hofer, G. Paltauf, M. Haltmeier, and O. Scherzer, "Thermoacoustic tomography with integrating area and line detectors", IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 52 (2005)], that uses line shaped detectors instead of the usual point like ones. We show that the three dimensional thermoacoustic imaging problem reduces to the mathematical problem of reconstructing the initial data of the two dimensional wave equation from boundary measurements of its solution. We derive and analyze an analytic reconstruction formula which allows for fast numerical implementation.