After describing a well-known method in radio astronomy called maximum-entropy imaging, I introduced a new method that also uses the maximum-entropy concept in a new way. The main distinction between these two approaches is that the well-known approach uses the entropy functional as a means of regularizing the data inversion in order to produce well-resolved images of point objects - stars in the case of radio astronomy. The new method uses the entropy functional not as a smoother or regularizer, but rather as the imaging criterion. When the entropy functional is maximum, or equivalently when our modified functional vanishes at some point in space, that is the location of a target. By plotting the inverse of this modified functional, we arrive at a method that has much in common with the MUSIC algorithm for imaging, but the new method uses different data. MUSIC requires the computation of the SVD of the response matrix. The new method can make use of this information if available, but does not require it. Furthermore, the new method can make use of just the diagonal elements of the response matrix (as in synthetic aperture imaging), or it can be used with time domain amplitude data for the main arrivals.
Future work on this approach will explore how robust the method is when the propagating medium is itself random, in addition to the presence of the isolated scatterers/targets we want to localize.