提升格式:多项式拟合的预测方法

Lifting Scheme: Prediction by Polynomial Fitting

本文研究提升格式中预测算子的设计问题。目前大多数预测算子,就其本质而言,属于插值预测的范畴。本文提出拟合预测的方法。从计算数学的角度来说,是插值的自然延伸。从提升格式的应用来说,数据的拟合曲线比数据的插值曲线更能代表数据包络线的低频成分。因此在某个局部,数据减去它的拟合预测值(而不是插值预测值),更能体现提升格式的预测过程应该是局域高通滤波的设计原则。本文提供了四点二次、六点二次和六点三次多项式拟合的计算实例。

The problem concerned in this paper is the design of predictor in Lifting Scheme. At present, most predictors, in essence, belong to the category of the interpolating prediction. Curve fitting is a natural extension of interpolating when seen from the aspect of computational mathematics. From the view of application of Lifting Scheme, the fitting curve can contain more low frequency components of a specific data's contour than the interpolating curve. It is therefore the design principle of the local high frequency filter that the error between the original data and its predicted value by curve fitting could better embody the prediction step in Lifting Scheme.