Naidu, R. Ramu and Jampana, Phanindra Varma and Sastry, Challa Subrahmanya
(2016)
Deterministic Compressed Sensing Matrices: Construction via Euler Squares and Applications.
IEEE Transactions on Signal Processing, 64 (14).
pp. 3566-3575.
ISSN 1053-587X
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Abstract
In compressed sensing the matrices that satisfy the
Restricted Isometry Property (RIP) play an important role. To
date, however, very few results for designing such matrices are
available. For applications such as multiplier-less data compres-
sion, binary sensing matrices are of interest. The present paper
constructs deterministic and binary sensing matrices using Euler
Squares. In particular, given a positive integer
m
different from
p, p
2
for a prime
p
, we show that it is possible to construct a
binary sensing matrix of size
m
×
c
(
mμ
)
2
,where
μ
is the coher-
ence parameter of the matrix and
c
∈
[1
,
2)
. The matrices that
we construct have small density (that is, percentage of nonzero en-
tries in the matrix is small) with no function evaluation in their
construction, which support algorithms with low computational
complexity. Through experimental work, we show that our binary
sensing matrices can be used for such applications as content based
image retrieval. Our simulation results demonstrate that the Eu-
ler Square based CS matrices give better performance than their
Gaussian counterparts.
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