Measurement matrix construction based on empirical mode decomposition

In order to maintain the integrity information on the signal in high probability, the measuremental matrix is designed to be a random one. But this randomness results in the fact that both useful information and useless information are near the equiprobably measured, which leads to a low sensing efficiency. To improve the sensing efficiency, this paper proposes a new method of measurement matrix construction based on Empirical Mode Decomposition of the reference signal. It uses the Intrinsic Mode Function to construct a cyclic matrix, which is proved to satisfy the restricted isometry property condition by the Gersgorin disc theorem. It simulates the signal denoising process and uses signal noise reduction as the measure. Simulation results show: (1)it has a better effect on reducing noise by adding noise to the reference signal; (2)when the noisy signal and the reference signal are dislocated in the time domain, the effect of noise reduction is significantly decreased compared with the ideal condition. However, the reconstructed signal maintains its frequency information well, which is helpful in practical applications.