Replica Symmetry Breaking in Compressive Sensing

Conference contribution
(Conference Contribution)

Publication Details

Author(s): Bereyhi A, Schulz-Baldes H, Müller R
Publisher: IEEE
Publication year: 2017
Pages range: 1 - 7
ISBN: 978-1-5090-5293-6
Language: English


For noisy compressive sensing systems, the asymptotic distortion with respect
to an arbitrary distortion function is determined when a general class of
least-square based reconstruction schemes is employed. The sampling matrix is
considered to belong to a large ensemble of random matrices including i.i.d.
and projector matrices, and the source vector is assumed to be i.i.d. with a
desired distribution. We take a statistical mechanical approach by representing
the asymptotic distortion as a macroscopic parameter of a spin glass and
employing the replica method for the large-system analysis. In contrast to
earlier studies, we evaluate the general replica ansatz which includes the RS
ansatz as well as RSB. The generality of the solution enables us to study the
impact of symmetry breaking. Our numerical investigations depict that for the
reconstruction scheme with the "zero-norm" penalty function, the RS fails to
predict the asymptotic distortion for relatively large compression rates;
however, the one-step RSB ansatz gives a valid prediction of the performance
within a larger regime of compression rates.

FAU Authors / FAU Editors

Bereyhi, Ali
Lehrstuhl für Digitale Übertragung
Müller, Ralf Prof. Dr.-Ing.
Professur für Informationsübertragung
Schulz-Baldes, Hermann Prof. Dr.
Professur für Mathematik (Mathematische Physik)

How to cite

Bereyhi, A., Schulz-Baldes, H., & Müller, R. (2017). Replica Symmetry Breaking in Compressive Sensing. In Proceedings of the Information Theory and Applications Workshop (ITA) (pp. 1 - 7). San Diego, CA, US: IEEE.

Bereyhi, Ali, Hermann Schulz-Baldes, and Ralf Müller. "Replica Symmetry Breaking in Compressive Sensing." Proceedings of the Information Theory and Applications Workshop (ITA), San Diego, CA IEEE, 2017. 1 - 7.


Last updated on 2019-21-07 at 07:26