  In Compressed Sensing the matrices that satisfy the Restricted Isometry
Property (RIP) play an important role. But to date, very few results for
designing such matrices are available. For applications such as multiplier-less
data compression, binary sensing matrices are of interest. The present work
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
$m \times c (m\mu)^2$, where $\mu$ is the coherence parameter of the matrix and
$c \in [1,2)$. The matrices that we construct have smaller density (that is,
percentage of nonzero entries 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 Euler Square based CS
matrices give better performance than their Gaussian counterparts.
