  We propose a new class of probabilistic reversing operations on the state of
a system that was disturbed by a weak measurement. It can approximately recover
the original state from the disturbed state especially with an additional
information gain using the Hermitian conjugate of the measurement operator. We
illustrate the general scheme by considering a quantum measurement consisting
of spin systems with an experimentally feasible interaction and show that the
reversing operation simultaneously increases both the fidelity to the original
state and the information gain with such a high probability of success that
their average values increase simultaneously.
