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Two are better than one: Fundamental parameters of frame coherence

Publication ,  Journal Article
Bajwa, WU; Calderbank, R; Mixon, DG
Published in: Applied and Computational Harmonic Analysis
July 1, 2012

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.

Duke Scholars

Published In

Applied and Computational Harmonic Analysis

DOI

EISSN

1096-603X

ISSN

1063-5203

Publication Date

July 1, 2012

Volume

33

Issue

1

Start / End Page

58 / 78

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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Bajwa, W. U., Calderbank, R., & Mixon, D. G. (2012). Two are better than one: Fundamental parameters of frame coherence. Applied and Computational Harmonic Analysis, 33(1), 58–78. https://doi.org/10.1016/j.acha.2011.09.005
Bajwa, W. U., R. Calderbank, and D. G. Mixon. “Two are better than one: Fundamental parameters of frame coherence.” Applied and Computational Harmonic Analysis 33, no. 1 (July 1, 2012): 58–78. https://doi.org/10.1016/j.acha.2011.09.005.
Bajwa WU, Calderbank R, Mixon DG. Two are better than one: Fundamental parameters of frame coherence. Applied and Computational Harmonic Analysis. 2012 Jul 1;33(1):58–78.
Bajwa, W. U., et al. “Two are better than one: Fundamental parameters of frame coherence.” Applied and Computational Harmonic Analysis, vol. 33, no. 1, July 2012, pp. 58–78. Scopus, doi:10.1016/j.acha.2011.09.005.
Bajwa WU, Calderbank R, Mixon DG. Two are better than one: Fundamental parameters of frame coherence. Applied and Computational Harmonic Analysis. 2012 Jul 1;33(1):58–78.
Journal cover image

Published In

Applied and Computational Harmonic Analysis

DOI

EISSN

1096-603X

ISSN

1063-5203

Publication Date

July 1, 2012

Volume

33

Issue

1

Start / End Page

58 / 78

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics