Two are better than one: Fundamental parameters of frame coherence

Published

Journal Article

This paper investigates two parameters that measure the coherence of a frame: worst-case and average coherence. We first use worst-case and average coherence to derive near-optimal probabilistic guarantees on both sparse signal detection and reconstruction in the presence of noise. Next, we provide a catalog of nearly tight frames with small worst-case and average coherence. Later, we find a new lower bound on worst-case coherence; we compare it to the Welch bound and use it to interpret recently reported signal reconstruction results. Finally, we give an algorithm that transforms frames in a way that decreases average coherence without changing the spectral norm or worst-case coherence. © 2011 Elsevier Inc. All rights reserved.

Full Text

Duke Authors

Cited Authors

  • Bajwa, WU; Calderbank, R; Mixon, DG

Published Date

  • July 1, 2012

Published In

Volume / Issue

  • 33 / 1

Start / End Page

  • 58 - 78

Electronic International Standard Serial Number (EISSN)

  • 1096-603X

International Standard Serial Number (ISSN)

  • 1063-5203

Digital Object Identifier (DOI)

  • 10.1016/j.acha.2011.09.005

Citation Source

  • Scopus