  A novel method to solve inverse problems for the wave equation is introduced.
The method is a combination of the boundary control method and an iterative
time reversal scheme, leading to adaptive imaging of coefficient functions of
the wave equation using focusing waves in unknown medium. The approach is
computationally effective since the iteration lets the medium do most of the
processing of the data.
  The iterative time reversal scheme also gives an algorithm for constructing
boundary controls for which the corresponding final values are as close as
possible to the final values of a given wave in a part of the domain, and as
close as possible to zero elsewhere. The algorithm does not assume that the
coefficients of the wave equation are known.
