# Aspects of Thermoacoustic Tomography

Marechal, Pierre

### Abstract

Thermoacoustic Tomography (TAT) is a non invasive imaging modality *TeX Embedding failed!*, which can be used in various domains such as medical imaging or small animal imaging. It can be described as follows: the sample to be imaged is illuminated by a pulsed electromagnetic energy, which results in a non-uniform thermoelastic expansion. The emitted pressure wave depends on the distribution of absorbed energy *TeX Embedding failed!*, and the inverse problem one is then facing is that of recovering *TeX Embedding failed!* from measurements of the acoustic signals performed outside the sample.

In this talk, we shall first review various aspects of the modelling of TAT, and then consider several issues concerning the reconstruction problem. We shall then discuss an approach based on the notion of regularization by mollification *TeX Embedding failed!*.

Joint work with Xavier Bonnefond.

**References:**

[1] *TeX Embedding failed!* and *TeX Embedding failed!*, *A variational approach to the inversion of truncated Fourier operators<\i> Inverse Problems, 2009. *

[2] *TeX Embedding failed!* and *TeX Embedding failed!*, *A variational approach to the inversion of some compact operators*, Pacific Journal of Optimization, **5(1)**, pp. 97-110, 2009.

[3] *TeX Embedding failed!* and *TeX Embedding failed!*, *Thermoacoustic CT: imaging principles*, Proceedings of the SPIE, **3916**, pp. 150-159, 2000.

[4] *TeX Embedding failed!* and *TeX Embedding failed!*, *A mollifier method for linear operator equations of the first kind*, Inverse Problems **6**, pp. 427-440, 1990.

[5] *TeX Embedding failed!* and *TeX Embedding failed!*, *Variational Methods in Imaging*, Springer Verlag (New York), Applied Mathematical Sciences, **167**, 2008.

### Details

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