Autoregressive process parameter estimation from compressed sensing measurements

In this paper we introduce a least squares estimator of the regression coefficients of an autoregressive process acquired by means of Compressed Sensing (CS). Unlike common CS problems in which we only know that the signal is sparse, using the proposed autoregressive model we can gain knowledge about the structure of the original signal without recovering it. This problem is addressed by introducing an ad-hoc sensing matrix able to preserve the structure of the regression. We numerically validate the performance of this matrix. Moreover, we present applications that naturally exploit this additional information we can directly obtain from the compressed data, and particularly power spectral density estimation from CS measurements.