Constructions Of Compressed Sensing Matrix Via Subspaces Of Symplectic Geometry And Pseudo-Symplectic Geometry

Compressed sensing theory provides a new approach to acquire data as a sampling technique and makes it possible that a sparse signal can be exactly or nearly exactly reconstructed from fewer measurements. The construction of compressed matrix which plays an important role in sampling and reconstruction of signals is a core problem in compressed sensing theory. The deterministic matrices based on geometry of classical groups over finite fields are constructed which satisfy restrict isometry property induced by low relevance.1. The construction of compressed sensing matrices1? and2? are based on the subspaces of symplectic space and singular symplectic space are provided and compared with the matrix ? constructed by DeVore based on polynomials over finite field.2. The matrix with some disjunctive and inclusive properties is constructed to efficiently restore signals together with a given algorithms which are based on singular symplectic space.