Time reversed absorbing condition: recreate the past and application to inverse problems
F. Assous, M. Kray, F. Nataf*



We introduce time reversed absorbing conditions (TRAC) in time reversal methods. They enable one to "recreate the past" without knowing the source which has emitted the signals that are back-propagated. We present two applications in inverse problems: the reduction of the size of the computational domain and the determination, from boundary measurements, of the location and volume of an unknown inclusion. The method does not rely on any a priori knowledge of the physical properties of the inclusion. Numerical tests with the wave equation illustrate the efficiency of the method. This technique is fairly insensitive with respect to noise in the data.

Reference : F. Assous, M. Kray, F. Nataf, E. Turkel, Time Reversed Absorbing Condition: Application to inverse problem, Inverse Problems (2011), Vol. 27, no 6.