Predictive transform: a simple and optimum unified approach to signal modeling, coding, estimation, and control

The decoder of a minimum mean-square-error predictive transform (PT) coder is found to be the key to a simple and optimum unification and transformation enhancement of well-established techniques in linear and nonlinear signal modeling, coding, estimation, and control. The fundamental property of the PT decoder that makes this possible is that the PT decoder is a whitening model of the signal that one wishes to model, encode, estimate, and/or control. In addition, the PT decoder is capable of exactly identifying a large class of linear and nonlinear whitening signal sources. Hence, this whitening signal modeling property of the PT decoder allows its integration with well-known signal-processing techniques such as Kalman estimation and linear quadratic Gaussian (LQG) control. An added bonus of this integration is the appearance of a transformation mechanism that leads to significant simplifications of the Kalman estimator as well as the LQG controller. The transformation-enhanced Kalman estimator is illustrated with monochrome images embedded in additive white noise and is found to produce a design and implementation complexity that is simpler than that of a classical Kalman estimator-without transformation-by a factor that approaches four in the smoothing case