Towards optimization of toeplitz matrices for compressed sensing

Compressed sensing is a new theory that samples a signal below the Nyquist rate. While Gaussian and Bernoulli random measurements perform quite well on the average, structured matrices such as Toeplitz are mostly used in practice due to their simplicity. However, the signal compression performance may not be acceptable. In this paper, we propose to optimize the Toeplitz matrices to improve its compression performance to recover sparse signals. We establish the optimization on minimizing the coherence of the measurement matrix by an intelligent optimization method called Particle Swarm Optimization. Our simulation results show that the optimized Toeplitz matrix outperforms the non-optimized one in reconstructing sparse signals in terms of quality and sampling rate.