Two are better than one: Fundamental parameters of frame coherence

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• 作者：Waheed U. Bajwa^a ; Robert Calderbank^b ; ^c ; Dustin G. Mixon^c ; ^{dmixon@princeton.edu}
• 关键词：Frames ; Worst-case coherence ; Average coherence ; Welch bound ; Sparse signal processing
• 刊名：Applied and Computational Harmonic Analysis
• 出版年：2012
• 期刊代码：119_10635203
• 类别：cp
• 出版时间：July, 2012
• 卷：33
• 期：1
• 页码：58-78
• 文件大小：339 K

摘要

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.