Structures and algorithms for two-dimensional adaptive signal processing

The focus of this work is to explore structures and algorithms for two-dimensional adaptive signal processing. Applications in image and multichannel signal processing include 2-D adaptive differential pulse code modulation, interference cancellation, predictive coding, and noise suppression. Emphasis is placed both on FIR and IIR structures with primary benchmark issues being speed of convergence, computational complexity, and structural flexibility.The behavior of the 2-D, FIR, direct form adaptive filter is analogous to that of its 1-D counterpart. Eigenvalue disparity of the input autocorrelation matrix hinders the performance of the steepest descent adaptive algorithm. By implementing a Gauss-Newton sequential adaptive algorithm, the adaptive "modes" are effectively orthogonalized and normalized, thereby increasing the speed of convergence. An efficient block Levinson algorithm is utilized to implement the required matrix operations giving a fast quasi-Newton algorithm (FQN) with O($N\sp3$) complexity. The method exploits the Toeplitz-block Toeplitz structure of the resulting autocorrelation matrix estimate and realizes further computational savings by assuming that the autocorrelation matrix is constant over blocks of $N\sp2$ iterations. The FQN filter is compared to the 2-D transform domain filter, the McClellan transformation filter, and the 2-D recursive least squares filter.Two-dimensional infinite impulse response adaptive filters are also examined. It is found that 2-D IIR adaptive filters are plausible and useful. They exhibit convergence behavior which is dependent upon the 2-D indexing scheme. Several useful indexing methods are examined. A quasi-Newton acceleration algorithm is developed for this structure using the same method as above, except that some additional constraints must be imposed on the 2-D IIR autocorrelation matrix. The 2-D IIR error surface is not quadratic, and must be examined for the possible existence of local minima. Some preliminary results are presented. However, error surfaces can be graphically examined in the three-dimensional coefficient space for IIR filters with first-order denominators. Finally some applications are presented which utilize 2-D IIR adaptive filters. These include 2-D ADPCM and interference cancellation.U of I OnlyETDs are only available to UIUC Users without author permissio