Discrimination theory of wavelet filters with learning ability

具有学习能力的小波滤波器是美国朗讯科技公司的研究员Sweldens提出的提升小波滤波器。提升小波滤波器由双正交分析滤波器和综合滤波器组成。使用分析滤波器将信号分解为低通和高通分量，并且可以使用合成滤波器从低通和高通分量重构原始信号。这意味着原始信号等效于分解的低通和高通分量。通过在双正交小波滤波器的基础上增加提升滤波器，构造了提升小波滤波器。提升滤波器中包含了可根据信号和图像自适应确定的自由参数，本文提出了几种自适应于信号和图像特定部分的自由参数学习方法，并建立了一种提取与特定部分相似片段的判别理论。在此基础上，提出了一种基于该学习方法的脉冲噪声抑制方法.在此基础上，利用小波多分辨率分析的思想，提出了一种快速的三维曲面简化算法。

Wavelet filters with learning ability indicate lifting wavelet filters proposed by Sweldens who is a researcher at Lucent Technology in USA. The lifting wavelet filters are consist of biorthogonal analysis and synthesis filters. A signal is decomposed into lowpass and highpass components using the analysis filter, and the original signal can be reconstructed from the lowpass and highpass components using the synthesis filter. This means that the original signal is equivalent to the decomposed lowpass and highpass components. The lifting wavelet filters are constructed by adding lifting filters to biorthogonal wavelet filters. The lifting filter contains free parameters which can be determined adaptive to signals and images.In our research, we proposed several learning methods of the free parameters adaptive to specific parts of signals and images, and established a discrimination theory for extracting pieces similar to the specific parts. We also presented an impulse noise reduction method based on our learning method. Furthermore, we proposed a fast simplification algorithm for generating 3D surfaces by using an idea of multiresolution analysis of wavelets.