Math @ Duke

Publications [#235984] of Robert Calderbank
Papers Published
 Mixon, DG; Bajwa, WU; Calderbank, R, Frame coherence and sparse signal processing,
IEEE International Symposium on Information Theory  Proceedings
(2011),
pp. 663667 [doi]
(last updated on 2017/12/17)
Abstract: The sparse signal processing literature often uses random sensing matrices to obtain performance guarantees. Unfortunately, in the real world, sensing matrices do not always come from random processes. It is therefore desirable to evaluate whether an arbitrary matrix, or frame, is suitable for sensing sparse signals. To this end, the present paper investigates two parameters that measure the coherence of a frame: worstcase and average coherence. We first provide several examples of frames that have small spectral norm, worstcase coherence, and average coherence. Next, we present a new lower bound on worstcase coherence and compare it to the Welch bound. Later, we propose an algorithm that decreases the average coherence of a frame without changing its spectral norm or worstcase coherence. Finally, we use worstcase and average coherence, as opposed to the Restricted Isometry Property, to garner nearoptimal probabilistic guarantees on both sparse signal detection and reconstruction in the presence of noise. This contrasts with recent results that only guarantee noiseless signal recovery from arbitrary frames, and which further assume independence across the nonzero entries of the signalin a sense, requiring small average coherence replaces the need for such an assumption. © 2011 IEEE.


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