积分-微分wave equation衰减模型的热声层析成像
Thermoacoustic tomography for an integro-differential wave equation modeling attenuation
摘要：
在这篇文章中，我们研究了热声层析成像（TAT）的逆问题的衰减表示的时间卷积（或记忆）的条款，其考虑的动机是通过分数阶导数的空间依赖参数的非均匀组织中的超声波建模。在能够测量整个边界上的数据的假设下，我们证明了唯一性和稳定性，并提出了一类光滑可变声速的收敛重建方法。通过对时间反演技术的适当修改，我们得到了一个Neumann级数重建公式。
英文摘要：
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.
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