  We study theoretically the mutual information between reflected and
transmitted speckle patterns produced by wave scattering from disordered media.
The mutual information between the two speckle images recorded on an array of N
detection points (pixels) takes the form of long-range intensity correlation
loops, that we evaluate explicitly as a function of the disorder strength and
the Thouless number g. Our analysis, supported by extensive numerical
simulations, reveals a competing effect of cross-sample and surface spatial
correlations. An optimal distance between pixels is proven to exist, that
enhances the mutual information by a factor Ng compared to the single-pixel
scenario.
