  Linear problems appear in a variety of disciplines and their application for
the transmission matrix recovery is one of the most stimulating challenges in
biomedical imaging. Its knowledge turns any random media into an optical tool
that can focus or transmit an image through disorder. Here, converting an
input-output problem into a statistical mechanical formulation, we investigate
how inference protocols can learn the transmission couplings by
pseudolikelihood maximization. Bridging linear regression and thermodynamics
let us propose an innovative framework to pursue the solution of the
scattering-riddle.
