| System modeling has proved to be very useful in signal processing. For two-dimensional (2-D) signal processing, system modeling or identification has applications in many areas, such as processing of satellite photographs, image communications, radar maps, seismic data imaging and medical X-ray imaging. In general, accurate system modeling is important in signal restoration applications, and efficient signal representation plays a key role in data compression. In this research, a linear algorithm for two-dimensional least-square approximation in the frequency domain is developed. The algorithm is based on the equation error model, and the approximation yields a two-dimensional rational function in the complex variables, or equivalently a two-dimensional auto-regressive, moving-average (ARMA) process. The important existence, uniqueness and convergence properties associated with this two-dimensional approximation problem are also discussed. This two-dimensional, least-square, frequency domain (2D-LS-FD) algorithm can accurately model a 2-D linear and shift invariant (LSI) stable system when the model has a sufficient order relative to the unknown and the identification noise is negligible. It is also capable of efficiently representing 2-D signals and images. The 2D-LS-FD has been modified and successfully applied to image restoration and 2-D dominant spectrum component representation applications. Based on the 2D-LS-FD algorithm, a 2-D, frequency domain, adaptive system modeling technique is developed with signal dependent, optimal convergence factors. This adaptive system modeling approach is further extended to design 2-D optimal predictors. This results in a new 2-D, frequency domain, motion compensation technique for video signal compression applications. Computer simulation results are given to verify the proposed techniques and also to demonstrate their superior performances when the proposed techniques are applied in some important application areas including 2-D system identification, image restoration, 2-D system tracking, 2-D spectral analysis and representation, and motion compensation for 3-D spatiotemporal signal compression. |
