# Mathematical Challenges Arising in Thermoacoustic Tomography with Line Detectors

@article{Haltmeier2006MathematicalCA, title={Mathematical Challenges Arising in Thermoacoustic Tomography with Line Detectors}, author={Markus Haltmeier and Thomas Fidler}, journal={arXiv: Analysis of PDEs}, year={2006} }

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…

## 9 Citations

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A new Radon-type transform to reconstruct the initial density function of photoacoustic tomography is proposed, based on the properties of Bessel functions and Fourier–Bessel series expansion.

### Thermoacoustic tomography with circular integrating detectors

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Heutzutage sind bildgebende Verfahren sehr wichtig f¨ur die medizinische Diagnostik.
Ein neues vielversprechendes Verfahren ist die Thermoakustische
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Thermoacoustic computed tomography provides a novel and promising technology in medical imaging. It is based on the generation of acoustic waves inside tissues by stimulation with electromagnetic…

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The article presents a survey of mathematical problems, techniques and challenges arising in thermoacoustic tomography and its sibling photoacoustic tomography.

### KACZMARZ METHODS FOR REGULARIZING NONLINEAR ILL-POSED EQUATIONS I: CONVERGENCE ANALYSIS

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In this article we develop and analyze novel iterative regularization techniques for the solution of systems of nonlinear ill-posed operator equations. The basic idea consists in considering…

### Inversion of Spherical Means and the Wave Equation in Even Dimensions

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We establish inversion formulas of the so-called filtered back-projection type to recover a function supported in the ball in even dimensions from its spherical means over spheres centered on the…

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