On reconstruction formulas and algorithms for the thermoacoustic tomography
M. Agranovsky, P. Kuchment, L. Kunyansky
TL;DR
This paper reviews recent advances in mathematical methods for thermoacoustic tomography, focusing on uniqueness, inversion formulas, and algorithms for solving the inverse wave equation problem, especially with constant sound speed.
Contribution
It surveys recent progress in establishing uniqueness and developing inversion formulas and algorithms for thermoacoustic tomography, emphasizing the spherical mean transform case.
Findings
Summarizes recent theoretical developments in inversion formulas.
Highlights algorithms for reconstructing images in thermoacoustic tomography.
Discusses the mathematical challenges of the inverse wave equation problem.
Abstract
The paper surveys recent progress in establishing uniqueness and developing inversion formulas and algorithms for the thermoacoustic tomography. In mathematical terms, one deals with a rather special inverse problem for the wave equation. In the case of constant sound speed, it can also be interpreted as a problem concerning the spherical mean transform.
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Taxonomy
TopicsPhotoacoustic and Ultrasonic Imaging · Advanced X-ray and CT Imaging · Thermography and Photoacoustic Techniques