Replica Symmetry Breaking in Compressive Sensing

Bereyhi A, Schulz-Baldes H, Müller R (2017)

Publication Language: English

Publication Type: Conference contribution, Conference Contribution

Publication year: 2017

Publisher: IEEE

Pages Range: 1 - 7

Event location: San Diego, CA US

ISBN: 978-1-5090-5293-6

DOI: 10.1109/ITA.2017.8023461

Open Access Link: https://arxiv.org/pdf/1704.08013.pdf

Abstract

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.

Authors with CRIS profile

Ali Bereyhi Lehrstuhl für Digitale Übertragung Hermann Schulz-Baldes Professur für Mathematik (Mathematische Physik) Ralf Müller Professur für Informationsübertragung

How to cite

APA:

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.

MLA:

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.

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