Thermoacoustic Tomography with Variable Sound Speed
نویسنده
چکیده
We study the mathematical model of thermoacoustic tomography in media with a variable speed for a fixed time interval Œ0;T so that all signals issued from the domain leave it after time T . In case of measurements on the whole boundary, we give an explicit solution in terms of a Neumann series expansion. We give almost necessary and sufficient conditions for uniqueness and stability when the measurements are taken on a part of the boundary.
منابع مشابه
Thermoacoustic Tomography with Variable Sound Speed Plamen Stefanov and Gunther Uhlmann
We study the mathematical model of thermoacoustic tomography in media with a variable speed for a fixed time interval, greater than the diameter of the domain. In case of measurements on the whole boundary, we give an explicit solution in terms of a Neumann series expansion. We give necessary and sufficient conditions for uniqueness and stability when the measurements are taken on a part of the...
متن کاملAn Efficient Neumann Series-Based Algorithm for Thermoacoustic and Photoacoustic Tomography with Variable Sound Speed
We present an efficient algorithm for reconstructing an unknown source in Thermoacoustic and Photoacoustic Tomography based on the recent advances in understanding the theoretical nature of the problem. We work with variable sound speeds that might be also discontinuous across some surface. The latter problem arises in brain imaging. The algorithmic development is based on an explicit formula i...
متن کاملThermoacoustic Tomography Arising in Brain Imaging
We study the mathematical model of thermoacoustic and photoacoustic tomography when the sound speed has a jump across a smooth surface. This models the change of the sound speed in the skull when trying to image the human brain. We derive an explicit inversion formula in the form of a convergent Neumann series under the assumptions that all singularities from the support of the source reach the...
متن کاملA Family of Inversion Formulas in Thermoacoustic Tomography
We present a family of closed form inversion formulas in thermoacoustic tomography in the case of a constant sound speed. The formulas are presented in both time-domain and frequency-domain versions. As special cases, they imply most of the previously known filtered backprojection type formulas.
متن کاملThermoacoustic tomography with correction for acoustic speed variations.
Thermoacoustic tomography (TAT) is a technique that measures microwave-induced thermoacoustic waves at the boundary of biological tissue and generates images of internal microwave absorption distributions from the measurements. Existing reconstruction algorithms for TAT are based on the assumption that the acoustic properties in the tissue are homogeneous. Biological tissue, however, has hetero...
متن کامل