Endomorphic modelling for two-dimensional time-varying autoregressive model signals

Physical signals are often non-stationary. We assume that images are non-stationary and each pixel is the output of a different set of two-dimensional autoregressive (AR) model coefficients; therefore, texture cannot be characterised by applying AR modelling techniques to the entire image. A multistage modelling technique, which appears in the literature as "endomorphic modelling", is applied to this kind of signal. The signal is divided into sub-sets of samples and each sub-set is modelled using an AR model. A new image is formed using the same AR model coefficient estimated from different blocks, then the new image is re-modelled using AR models again. This process ends when the variance of the estimated parameters is sufficiently small. The simulation results show that the variances obtained from the estimated coefficients at the second stage are much smaller than the ones from the first stage