Predictive transform estimation [image processing]

Minimum mean squared error (MSE) linear predictive transform (LPT) source decoding (or modeling) and Kalman estimation are integrated to yield a unified approach to source modeling and estimation called PT estimation. PT estimation enhances classical Kalman estimation in two ways: first, it directly addresses the source modeling problem of scalar or multidimensional Kalman estimation by integrating an exact minimum MSE LPT decoder with a Kalman estimator; second, it provides a transformation mechanism that inherently leads to significant design and implementation simplifications when the state dimensionality is large. In the specific case of image reconstruction, the design and implementation requirements of 2-D LPT smoother structures are lessened with respect to those of classical 2-D Kalman smoother structures with exactly equivalent performance by factors that approach eight and four, respectively. Simple nonadaptive 2-D LPT smoothers perform quite well when compared with previous adaptive linear minimum MSE estimators