基于小波的曲线可控误差拟合

研究了利用小波变换对所拟合曲线进行分解和重构的方法,给出了进行曲线拟合的误差控制,采用Daubechies小波对所拟合曲线进行快速小波变换。通过分层近似对原曲线进行拟合,所产生的误差刚好为高频滤掉部分。在构造近似曲线前,通过对曲线细节的预先计算,得出可控制误差的范围,从而决定是否继续进行曲线的细化分解,达到在可控制误差下进行曲线拟合的目的。文中给出了基于小波的曲线可控误差拟合算法,并用实例进行了说明。

Wavelet-based Curve Fitting under the Controllable Error

A method for curve fitting under the control of tolerance errors is studied based on wavelet transform.In which the curve is decomposed into wavelet coefficients and scale coefficients with different scale,fast wavelet transform is applied to curve fitting with Daubechies wavelet.Similar curve in every decomposed level can be obtained,as a filtered high frequency,the details is just tolerance error of the curve.So before constructing a similar curve,we can calculate details of the curve,according to the error resulted from last step,then decide whether decomposed processes go on or not,curve fitting can be done as our desirablility.An algorithm is described and an example is illustrated to this method here.