Publications [#235749] of Robert Calderbank

Journal articles or Book chapters PUBLISHED
  1. Calderbank, R; Thompson, A; Xie, Y, On block coherence of frames, Applied and Computational Harmonic Analysis, vol. 38 no. 1 (January, 2014), pp. 50-71 [doi] .

    © 2014 Elsevier Inc. All rights reserved. Block coherence of matrices plays an important role in analyzing the performance of block compressed sensing recovery algorithmns (Bajwa and Mixon, 2012). In this paper, we characterize two block coheremice 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 mnatrix is constrained to be a union of orthobases. We then present determninistic mnatrix constructions based upon Kronecker products which obtain these lower bounds. We also characterize the worst-case block coherence of randomn suibspaces. Finally, we present a flipping algorithmn that can imnprove the average block coherence of a mnatrix, w}ule mnaintaining the worst- case block coherence of the original mnatrix. We provide nuimnerical examnples which demnonstrate that our proposed determninistic mnatrix construction performns well in block comnpressed sensing.