Deterministic compressed sensing matrices: Construction via Euler Squares and applications

TL;DR

This paper introduces a method to construct deterministic, binary sensing matrices using Euler Squares for compressed sensing, which are computationally efficient and outperform Gaussian matrices in image retrieval tasks.

Contribution

It presents a novel deterministic construction of binary sensing matrices via Euler Squares, with improved density and performance for compressed sensing applications.

Findings

Matrices have smaller density and no function evaluations in construction.

Experimental results show better performance than Gaussian matrices.

Matrices are suitable for applications like content-based image retrieval.

Abstract

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.