Two-dimensional autoregressive modeling by autocorrelation fitting and applications to signal processing
The purpose of this thesis is to extend the technique of one-dimensional (1-D) autoregressive (AR) modeling by autocorrelation function (ACF) fitting to the two-dimensional (2-D) case and investigate applications of these AR models in 2-D signal processing. In the process of the research, we have (1) discussed three different error criteria in signal modeling and presented the properties of the error criterion of autocorrelation fitting; (2) reviewed the 1-D AR modeling algorithm for ACF fitting and investigated the relationship of the algorithm with the Steiglitz-McBride system identification algorithm. The properties of the algorithm in fitting the ACF and power spectrum and in effective compensation and adaptive filtering of the observation noise are discussed; (3) extended the 1-D ACF fitting algorithm to obtain 2-D AR modeling algorithms for both nonsymmetric half plane and quarter plane supports. Initial model parameter determination and model stability checking using the Ekstrom-Woods spectral factorization approach are presented; (4) used the resulting 2-D AR models for 2-D spectral and frequency (or frequency-wavenumber) estimation. The ability of the AR models to provide improved estimates is analyzed theoretically and demonstrated by experiments; (5) used the resulting AR models for coding and processing of the Wigner distribution (WD). The effectiveness of the models in representing the original WD's and removing troublesome cross-terms is illustrated with applications to several typical WD signals; (6) presented some research topics for the further development of modeling techniques based on ACF fitting. ^
"Two-dimensional autoregressive modeling by autocorrelation fitting and applications to signal processing"
Dissertations and Master's Theses (Campus Access).