参数化小波构造研究及其在边缘检测中的应用

为了解决双正交小波构造过程中存在的局限性和不灵活性，以小波滤波器代数构造理论为基础，提出一种支集定长条件下双正交小波滤波器组的参数化构造方法，推导出高通分解滤波器支集长度为奇数或偶数情况下双正交小波滤波器组的构造限定条件，给出具体的参数化构造实例，并分析了参数变化对构造小波特性的影响。从小波特性出发分析了用于图像边缘检测的双正交小波的构造必要条件，结合参数化小波构造方法构建了用于图像边缘检测的小波滤波器组。仿真实例验证了双正交小波滤波器参数化构造方法的灵活性和可行性以及构造小波对图像边缘检测的有效性。

Research on Parameterized Design of Wavelet and Its Application in Edge Detection

To solve the inflexibility and the limitation of the biorthogonal wavelet construction,a filter banks parameterized design in case of a fixed support length is proposed which is based on filter banks algebraical construction method.The limiting conditions of biorthogonal wavelet filter banks construction are derived for cases when the filter length of high-pass decomposing filter banks is odd or even.According to the new construction method,some filter banks parameterized design examples are given.And the e...