Publications [#236004] of Robert Calderbank

Journal articles or Book chapters PUBLISHED
  1. Bajwa, WU; Calderbank, R; Mixon, DG, Two are better than one: Fundamental parameters of frame coherence, Applied and Computational Harmonic Analysis, vol. 33 no. 1 (2012), pp. 58-78 [doi] .

    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.