图学学报
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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
王 乔, 崔 丽. 小波分析中一类滤波器的构造[J]. 图学学报.
Wang Qiao, Cui Li. Construction of A Class of Filter in Wavelet Analysis[J]. Journal of Graphics.
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http://www.txxb.com.cn/CN/Y2015/V36/I2/257