Thermoacoustic tomography for an integro-differential wave equation modeling attenuation
Thermoacoustic tomography for an integro-differential wave equation modeling attenuation
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DOI：
10.1016/j.jde.2017.10.012
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发表时间：
2017-03
影响因子：
2.4
通讯作者：
Sebastián Acosta;Benjamin Palacios
中科院分区：
文献类型：
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作者：
Sebastián Acosta;Benjamin Palacios
在这篇文章中，我们研究了热声层析成像（TAT）的反问题，在一个衰减由时间卷积（或记忆）项表示的介质上，其考虑的动机是通过具有空间相关参数的分数阶导数在非均匀组织中对超声波进行建模。在能够在整个边界上测量数据的假设下，我们证明了唯一性和稳定性，并提出了一类光滑变声速的收敛重构方法。通过对时间反转技术进行适当的修正，得到了一个诺伊曼级数重构公式。
In this article we study the inverse problem of thermoacoustic tomography (TAT) on a medium with attenuation represented by a time-convolution (or memory) term, and whose consideration is motivated by the modeling of ultrasound waves in heterogeneous tissue via fractional derivatives with spatially dependent parameters. Under the assumption of being able to measure data on the whole boundary, we prove uniqueness and stability, and propose a convergent reconstruction method for a class of smooth variable sound speeds. By a suitable modification of the time reversal technique, we obtain a Neumann series reconstruction formula.