SIAM Journal on Mathematical Analysis, Volume 52, Issue 5, Page 5196-5212, January 2020.
The authors consider the problem of recovering an observable from certain measurements containing random errors. The observable is given by a pseudodifferential operator while the random errors are generated by a Gaussian white noise. The authors show how wave packets can be used to partially recover the observable from the measurements almost surely. Furthermore, they point out the limitation of wave packets to recover the remaining part of the observable and show how the errors hide the signal coming from the observable. The recovery results are based on an ergodicity property of the errors produced by wave packets.

中文翻译：

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噪声测量波包的观测极限

SIAM数学分析期刊，第52卷，第5期，第5196-5212页，2020年1月
。作者考虑了从包含随机误差的某些测量中恢复可观测值的问题。可观察值是由伪微分算子给出的，而随机误差是由高斯白噪声产生的。这组作者展示了如何使用波包几乎确定地从测量值中恢复出可观测的部分。此外，他们指出了波包在恢复可观测部分剩余部分方面的局限性，并显示了错误如何隐藏来自可观测部分的信号。恢复结果基于波包产生的错误的遍历性。