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

Time-reversal methods have attracted increasing interest recently. The so-called computational time-reversal approach creates an image of the illuminated scene by computing the back-propagated field and is useful for detecting and estimating targets in the scene. In Shi and Nehorai ["Maximum Likelihood Estimation of Point Scatterers for Computational Time-Reversal Imaging," Communications in Information and Systems, vol. 5, no. 2, pp. 227-256, 20051], we estimated point scatterers by maximum-likelihood estimate (MLE) using the Born-approximated physical model, as well as the Foldy-Lax model. In this correspondence, we further find an explicit relationship between energy-based basic time-reversal imaging and the MLE approach: the time-reversal imaging function differs by only a scaling factor from the likelihood imaging function using the estimated scattering potential when a single-scatterer model is employed. Furthermore, this scaling factor is a function of the imaging position only. We show that, as a result, time-reversal imaging has a near-far problem that tends to produce a weaker image for areas further away from the imaging arrays, whereas the MLE-based image is more balanced. Experimental results confirm this conclusion.