LAUSR

In this paper, we consider an inverse problem for the [Formula: see text]-dimensional random Schrödinger equation [Formula: see text]. We study the scattering of plane waves in the presence of a potential [Formula: see text] which is assumed to be a Gaussian random function such that its covariance is described by a pseudodifferential operator. Our main result is as follows: given the backscattered far field, obtained from a single realization of the random potential [Formula: see text], we uniquely determine the principal symbol of the covariance operator of [Formula: see text]. Especially, for [Formula: see text] this result is obtained for the full nonlinear inverse backscattering problem. Finally, we present a physical scaling regime where the method is of practical importance.