Constructions Of Deterministic Sensing Matrices Based On Vector Spaces And Singular Linear Spaces

As an emerging approach of signal processing with the rapid development of information technology, not only has compressed sensing(CS) successfully compressed and sampled signals with few measurements, but also has owned the capabilities of ensuring the exact recovery of signals. It is also famous for saving the storage spaces and avoiding wasting resources. As above-mentioned, it gets more and more considerable attention from all over the world. Actually, the(compressed) sensing matrices acts a significant in the CS theory,Hence the construction of sensing matrices is the key problem. In this paper, we efficiently combine the relative definitions of CS and the finite field to construct some kinds of deterministic compressive sensing matrices.1. The construction based on vector spaces.Given integers Let be the binary matrix, whose rows are indexed by the1m-dimensional vector subspaces of, whose columns are indexed by the m-dimensional vector subspaces ofn and with a 1 or 0 in the(i, j) position of the matrix,if the i-th1m-dimensional vector subspace is or is not contained in the j-th m- dimensional vector subspace, respectively. We will calculate the value of row, column, the sparsity k and the weight of column based on the counting formulas in the vector spaces and then compare our constructions with the pre-existing matrices through calculation and numerical simulations.2. The construction based on singular linear spaces.Based on singular linear spaces, we construct two kinds of deterministic compressive sensing matrices. Compare our constructions with the pre-existing matrices through calculation and numerical simulations with getting the relative parameters.