An Optimized Toeplitz Measurement Matrix based on ANN for Compressive Sensing ⋆

Compressive sensing takes advantage of the signals in some domain, allowing the entire signal to efficiently acquired and reconstructed from relatively few measurements. Toeplitz matrix has more advantages in the amount of data and computation over Gaussian random matrix, but its far from Gaussian matrix in the performance of signal reconstruction. In this paper, Toeplitz matrix is employed and optimized based on Artificial Neural Networks (ANN) in machine learning. The experimental results demonstrate that the proposed optimization method, compare with the Gaussian random matrix and the original matrix, the optimized matrix can reduce the amount of data and improve the CS performance in the meantime.