Low-complexity methods for autoregressive signal modeling

Abstract

Autoregressive (AR) models provide a means to approximate the spectrum of a signal. In this work, we face the problem of designing computationally efficient methods for parameter estimation in 1st and 2nd order AR processes. First, we review how the spectral distribution provides an analysis of the variance of a time series by revealing its frequency components. Then, we tackle the low-complexity parameter estimation problem in the AR(1) case using a binarized process and a piecewise linear curve approximation heuristic, whose multiplicative complexity does not depend on the blocklength. A comprehensive literature review on the binarized version of AR(1) processes is presented. An algorithm based on stochastic approximations is presented for estimating the parameters of AR(1) processes. We show that the resulting estimator is asymptotically equivalent to the exact maximum likelihood estimator. For moderately large samples (N > 100), the algorithm represents an economy of 50% in both additions and multiplications with respect to the direct method. For the AR(2) model, based on simulations, we show how estimates of its parameters can be obtained using two iterations of AR(1) filtering. We bootstrap our AR(1) methods to solve the low-complexity AR(2) parameter estimation problem. Such iterative estimation strategy displays competitive statistical behavior in simulations when compared to standard maximum likelihood estimates. Finally, the low-complexity estimator is experimented in the context of image segmentation. The autocorrelation of pixel intensity values of texture images is considered as a descriptive measure for textures. The low-complexity estimator has a smaller within variance than the exact estimator in 30% of the considered textures and a smaller within median absolute eviation in 46% of of the cases.