PREDICTIVE TRANSFORM ESTIMATION

In this paper it is shown that the source modeling problem of Kalman estimation is inherently addressed by the decoder of a recently offered multidimensional minimum mean squared error (MSE) linear predictive transform (LPT) source coding formulation. More specifically, it is demonstrated that the LPT decoder models the encoded source with whitening linear state space equations, i.e., linear state space equations driven either by a white or an approximately white vector disturbance. Furthermore, it is demonstrated that the LPT decoder has the desirable property of exactly identifying the source, when the source is characterized by white linear state space equations. Hence the LPT decoder is integrated with a Kalman estimator to yield a unified approach to scalar or multidimensional source modeling and estimation which is denoted here as predictive transform (PT) estimation. An added bonus of PT estimation is the appearance of a transformation mechanism that leads to significant design and implementation simplifications when the state dimensionality is large. The above ideas are illustrated with NTSC monochrome images where it is found that the design and implementation requirements of PT smoother structures are lessened, with respect to those of classical Kalman smoother structures with exactly equivalent performance, by factors that approach eight and four, respectively. Simple nonadaptive linear PT smoothers are also found to perform quite well when compared with previously offered adaptive linear minimum MSE estimators. The paper ends with a discussion of possible extensions of the present PT theory to other important areas such as control.