  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.
