[Landau ITP Seminars] Friday 12.04.2019

[Serge Krashakov]

Уважаемые сотрудники ИТФ,

В пятницу 12 апреля 2019 года состоится коллоквиум, на котором будет 
заслушан доклад:

Ян Фёдоров (King's College London)
*On reconstructing nonlinearly encrypted signals corrupted by noise.**
*
I consider the problem of reconstructing a source vector from its 
encrypted image corrupted by an additive Gaussian noise. Assuming 
encryption to be given by a random Gaussian mapping, the reconstruction 
problem in the framework of the Least Square Scheme turns out to be 
equivalent to finding the configuration of minimal energy in a certain 
version of spherical spin glass model. As a measure of the quality of 
the signal reconstruction one can use the mean overlap between the 
original signal and its recovered image. Thi overlap is analysed in the 
framework of Parisi scheme of Replica Symmetry Breaking. If the mapping 
is quadratic, there exists a threshold in the noise-to-signal ratio 
beyond which the reconstruction is impossible. The behaviour close to 
the threshold is controlled by the replica symmetry breaking mechanism 
and is characterized by a nontrivial exponent 3/4.
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