A relationship between time-reversal imaging and maximum likelihood scattering estimation

Time-reversal methods have attracted increasing interest recently with broad applications. In the so-called physical time-reversal methods, a transducer array first records a signal emitted by sources or reflected by targets, then it transmits the time-reversed and complex conjugated version of the measurements back into the medium. It was shown that the back-propagated wave would refocus around the locations of the sources or scatterers. This is attractive in many applications in which the energy of waves needs to be physically focused at the desired destinations, e.g., in secure communications or biomedical applications. Another way of employing the refocusing property is computational time-reversal imaging, in which the back-propagation process is simulated in a computer instead of implemented in a real medium. The power of the simulated back-propagated wave is used as the imaging metric, and the generated image can be applied to target detection and estimation, etc. In this paper, we derive an explicit relationship between the power-based computational time-reversal imaging, also called basic time-reversal imaging, and maximum likelihood estimate (MLE) of the scattering potential. We show that the metrics of the two imaging methods, though originate from different physical quantities, differ by only a scaling factor, which is a function of imaging position. We conclude that the time-reversal imaging has a near-far problem producing weaker image for the area that is further away from the imaging arrays, whereas the MLE-based image of the scattering potential is a more balanced thanks to the inherent appropriate scaling.