Аннотация:
We define a (symmetric key) encryption of a signal as a random mapping
known both to the sender and a recipient. In general the recipients may
have access only to images corrupted by an additive noise of unknown
strength. Given the encryption redundancy parameter and the signal
strength parameter, we consider the problem of reconstructing the signal
from its corrupted image by a Least Square Scheme for a certain class of
random Gaussian mappings. The problem is equivalent to finding the
configuration of minimal energy in a certain version of spherical spin
glass model, with squared Gaussian random interaction potential.
We use the Parisi replica symmetry breaking scheme for evaluating the
mean overlap between the original signal and its recovered image.
As a related, but separate problem, we will also briefly discuss the cost
function "landscape" in the simplest random Least Square optimization on a
sphere.
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