论文标题
多频逆介质问题的稳定性
Stability for the multifrequency inverse medium problem
论文作者
论文摘要
多频率1D反向介质问题的解包括从散射波的测量值中恢复介质的折射率，以实现多个频率。在本文中，当频率以界限为界的间隔时得出值时，得出了严格的稳定性估计。这表明，随着频率间隔的宽度变化，反向介质问题的不良性降低。更确切地说，在折射率的某些规律性假设下，估计值表明Hölder稳定性中的功率是频段中最大值的函数的增加。最后，对于通过截短的痕量公式定义的介质函数的可观察部分获得了Lipschitz稳定性估计。
The solution of a multi-frequency 1d inverse medium problem consists of recovering the refractive index of a medium from measurements of the scattered waves for multiple frequencies. In this paper, rigorous stability estimates are derived when the frequency takes value in a bounded interval.It is showed that the ill-posedness of the inverse medium problem decreases as the width of the frequency interval becomes larger. More precisely, under certain regularity assumptions on the refractive index, the estimates indicate that the power in Hölder stability is an increasing function of the largest value in the frequency band. Finally, a Lipschitz stability estimate is obtained for the observable part of the medium function defined through a truncated trace formula.
