Research on measurement matrix based on compressed sensing theory

Abstract

Compressed Sensing is for sparse and compressible signals, the data is compressed while the signal is sampled. This paper proposes the new deterministic measurement matrices that are studied: according to the compressible signal characteristics, we will use the unit matrix added with random orthogonal matrix and complementary sequences as the measurement matrix, and then using orthogonal matching pursuit (OMP) algorithm to reconstruct the signal, we can safely draw that as deterministic measurement matrix, they are feasible to reconstruct the original signal accurately. The simulation results show that the performances of the unit matrix added with random orthogonal matrix and complementary sequences are not only superior the partial Hadamard matrix, but also better than the Gaussian random measurement matrix.