Reconstructing Encrypted Signals: Optimization with input from Spin Glasses and RMT

I will consider the problem of reconstructing a signal from its encrypted and corrupted image
by a Least Square Scheme. For a certain class of random encryption the problem is equivalent to finding the
configuration of minimal energy in a (unusual) version of spherical spin
glass model.  The Parisi replica symmetry breaking (RSB) scheme is then employed for evaluating
the quality of the reconstruction. It  reveals a phase transition controlled
by RSB and reflecting impossibility of the signal retrieval beyond certain level of noise.