On singularities and instability of reconstruction in thermoacoustic tomography
On singularities and instability of reconstruction in thermoacoustic tomography
复制标题
热声层析成像重建的奇异性和不稳定性
DOI：
10.1090/conm/559/11078
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Linh V. Nguyen
中科院分区：
文献类型：
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作者：
Linh V. Nguyen
我们考虑热声层析成像（TAT）问题，其中需要从观测表面上的值重建波动方程解的初值。我们证明了如果方程的某些几何射线不与观测面相交，则在TAT中的重建不是H\ \{0}更稳定的。
We consider the problem of thermoacoustic tomography (TAT), in which one needs to reconstruct the initial value of a solution of the wave equation from its value on an observation surface. We show that if some geometric rays for the equation do not intersect the observation surface, the reconstruction in TAT is not H\"{o}lder stable.