Construction of compressed sensing matrixes based on the singular pseudo-symplectic space over finite fields

Compressed sensing (CS) provides a new approach to acquire data as a sampling technique and makes it sure that a sparse signal can be reconstructed from few measurements. The construction of compressed matrixes is a central problem in compressed sensing. This paper provides a construction of deterministic CS matrixes, which are also disjunct and inclusive matrixes, from singular pseudo-symplectic space over finite fields of characteristic 2. Our construction is superior to DeVore's construction under some conditions and can be used to reconstruct sparse signals through an efficient algorithm.