A resolution study for imaging and time reversal in random media

We consider the inverse problem of array imaging of active sources (targets) in randomly inhomogeneous media, in a remote sensing regime with significant multiple scattering of the waves by the inhomogeneities. The active source emits a pulse that propagates through the inhomogeneous medium and is captured by an array of aperture a that is far from the source. We consider an analytical model for the matched field imaging functional and study the effect of random inhomogeneities on the resolution of the images produced. In our model the effect of the random medium is quantified by a single parameter, the narrow-band effective aperture of the array ae. We give a robust procedure for estimating ae, which is of great interest in many applications. In time reversal, knowing ae allows us to estimate the refocused spot size, that is, the resolution of the time reversed, back-propagated field, which we can use in applications such as secure communications. The effective aperture ae quantifies in an explicit way the loss of resolution in imaging active sources embedded at unknown locations in a randomly inhomogeneous medium, as well as the gain in resolution beyond the diffraction limit, the super-resolution, in time reversal.