%A Jung,Peter
%A Kueng,Richard
%A Mixon,Dustin G.
%D 2019
%J Frontiers in Applied Mathematics and Statistics
%C
%F
%G English
%K compressed sensing,K-wise independence,Orthogonal array,Spherical design,Derandomization
%Q
%R 10.3389/fams.2019.00026
%W
%L
%N 26
%M
%P
%7
%8 2019-June-06
%9 Original Research
%#
%! compressed sensing with combinatorial design
%*
%<
%T Derandomizing Compressed Sensing With Combinatorial Design
%U https://www.frontiersin.org/article/10.3389/fams.2019.00026
%V 5
%0 JOURNAL ARTICLE
%@ 2297-4687
%X Compressed sensing is the art of effectively reconstructing structured n-dimensional vectors from substantially fewer measurements than naively anticipated. A plethora of analytical reconstruction guarantees support this credo. The strongest among them are based on deep results from large-dimensional probability theory and require a considerable amount of randomness in the measurement design. Here, we demonstrate that derandomization techniques allow for a considerable reduction in the randomness required for such proof strategies. More precisely, we establish uniform s-sparse reconstruction guarantees for Cs log(n) measurements that are chosen independently from strength-4 orthogonal arrays and maximal sets of mutually unbiased bases, respectively. These are highly structured families of C~n2 vectors that imitate signed Bernoulli and standard Gaussian vectors in a (partially) derandomized fashion.