We present a statistical framework for the fixed-frequency
computational time-reversal imaging problem assuming point
scatterers in a known background medium. Our statistical
measurement models are based on the physical models of the
multistatic response matrix, the distorted wave Born approximation
and Foldy-Lax multiple scattering models. We develop maximum
likelihood (ML) estimators of the locations and reflection
parameters of the scatterers. Using a simplified single-scatterer
model, we also propose a likelihood time-reversal imaging
technique which is suboptimal but computationally efficient and
can be used to initialize the ML estimation. We generalize the
fixed-frequency likelihood imaging to multiple frequencies, and
demonstrate its effectiveness in resolving the grating lobes of a
sparse array. This enables to achieve high resolution by deploying
a large-aperture array consisting of a small number of antennas
while avoiding spatial ambiguity. Numerical and experimental
examples are used to illustrate the applicability of our results.