MEM pixel correlated solutions for generalized moment and interpolation problems

We propose a new family of solutions for the classical generalized moment problem and the interpolation problem. The maximum entropy method on the mean (MEM) construction is the limit of the mean of some random discretized measure, where the amplitudes between pixels have a dependence structure. The method may be interpreted as a Bayesian procedure. Linear transfer allows one to introduce new prior information such as: modality, convexity, Sobolev norms. We also present MEM for exchangeable amplitudes on the pixels