Compressive modeling of stationary autoregressive processes

Compressive covariance sampling (CCS) methods that estimate the correlation function from compressive measurements have achieved great compression rates lately. In stationary autoregressive (AR) processes, the power spectrum is fully determined by the AR parameters, and vice versa. Therefore, compressive estimation of AR parameters amounts to CCS for such signals. However, previous CCS methods typically do not fully exploit the structure of AR power spectra. On the other hand, traditional AR parameter estimation methods cannot be used when only a compressed version of the AR signal is observed. We propose a Bayesian algorithm for estimating AR parameters from compressed observations, using a Metropolis-Hastings sampler. Simulation results confirm the promising performance of the proposed method.