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图学学报

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小波分析中一类滤波器的构造

  

  • 出版日期:2015-04-30 发布日期:2015-06-03

Construction of A Class of Filter in Wavelet Analysis

  • Online:2015-04-30 Published:2015-06-03

摘要: 通过对多分辨分析性质的讨论,提出了使用数值方法修正初始滤波器得到紧支集
正交滤波器的方法。可以针对任何紧支集滤波器进行迭代,自动得到消失矩更高、质量更优的
滤波器。基于Legendre 多项式,构造一组平移正交系,在得到初始滤波器后进行修正,获得消
失矩为2 的滤波器。与db3 小波进行处理一维信号和二维信号的对比检测,实验证明该滤波器
在图像边缘处理中有效。

关键词: 小波分析, 滤波器, 数值方法, 紧支集, Legendre 多项式

Abstract: This paper presents numerical methods of correcting the initial filters into compactly
supported orthogonal filters by the discussion of multi-resolution analysis. The algorithm can iterate
for any compactly supported filters, producing better quality filters with higher vanishing moment
automatically. Based on Legendre polynomials, we construct a set of translation orthogonal system,
and on the correction of certain initial filters, we obtain the filters with vanishing moment of two.
Then we make a detection on the obtained filters about dealing with one-dimensional signals and
two-dimensional signals by contrast with db3 wavelet, and the experiment proves that the filters have
an effect dealing with the edges of images.

Key words: wavelet, filter, numerical method, compactly supported, Legendre polynomials