  The time reversal symmetry of the wave equation allows wave refocusing back
at the source. However, this symmetry does not hold in lossy media. We present
a new strategy to compensate wave amplitude losses due to attenuation. The
strategy leverages the instantaneous time mirror (ITM) which generates reversed
waves by a sudden disruption of the medium properties. We create a
heterogeneous ITM whose disruption is unequal throughout the space to create
waves of different amplitude. The time-reversed waves can then cope with
different attenuation paths as typically seen in heterogeneous and lossy
environments. We consider an environment with biological tissues and apply the
strategy to a two-dimensional digital human phantom from the abdomen. A
stronger disruption is introduced where the forward waves suffer a history of
higher attenuation, with a weaker disruption elsewhere. Computer simulations
show heterogeneous ITM is a promising technique to improve time reversal
refocusing in heterogeneous, lossy, and dispersive spaces.
