Math @ Duke
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Publications [#235749] of Robert Calderbank
Papers Published
- Calderbank, R; Thompson, A; Xie, Y, On block coherence of frames, vol. 38 no. 1
(July, 2013),
pp. 50-71, ISSN 1063-5203 [doi]
(last updated on 2024/03/28)
Abstract: Block coherence of matrices plays an important role in analyzing the
performance of block compressed sensing recovery algorithms (Bajwa and Mixon,
2012). In this paper, we characterize two block coherence metrics: worst-case
and average block coherence. First, we present lower bounds on worst-case block
coherence, in both the general case and also when the matrix is constrained to
be a union of orthobases. We then present deterministic matrix constructions
based upon Kronecker products which obtain these lower bounds. We also
characterize the worst-case block coherence of random subspaces. Finally, we
present a flipping algorithm that can improve the average block coherence of a
matrix, while maintaining the worst-case block coherence of the original
matrix. We provide numerical examples which demonstrate that our proposed
deterministic matrix construction performs well in block compressed sensing.
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