Name
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. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1109/ITA.2017.8023461 | 2017 Information Theory and Applications Workshop (ITA) |
Keywords | DocType | Volume |
noisy compressive sensing systems,replica symmetry breaking,asymptotic distortion,arbitrary distortion function,least-square based reconstruction,sampling matrix,random matrix,i.i.d. matrix,projector matrix,source vector,statistical mechanical approach,macroscopic parameter,spin glass,large-system analysis,replica ansatz,zero-norm penalty function,one-step RSB ansatz | Conference | abs/1704.08013 |
ISBN | Citations | PageRank |
978-1-5090-5294-3 | 1 | 0.38 |
References | Authors | |
9 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Ali Bereyhi | 1 | 37 | 14.09 |
| R. Muller | 2 | 1206 | 124.92 |
| Hermann Schulz-Baldes | 3 | 5 | 1.22 |