不可分对称正交小波紧框架的构造

Construction of Nonseparable Orthogonal Wavelet Tight Frames with Symmetry

与可分小波相比,不可分小波更能捕捉高维信号的高频信息,正交框架在处理高维信号时能避免预滤波.为了更有效地处理高维信号,本文研究了不可分正交小波紧框架的构造,提出了一种由一维小波紧框架来构造高维不可分正交小波紧框架的方法,即先用张量积的方法构造高维小波紧框架,然后乘上一个具有一定性质的三角多项式.如果一维小波紧框架是对称的,用本文提出的方法构造的高维不可分的正交小波紧框架也是对称的.最后给出了一个构造算例.

Nonseparable wavelets can capture high frequency information of multi-dimensional signal compared with separable ones, and orthogonal frames can avoid pre-filtering in process-ing of multi-dimensional signal. In order to process multi-dimensional signal e？ciently, this paper studies the construction of nonseparable orthogonal wavelet tight frames constructed by unidimenstional one through tensor product, and multiplied by a trigonometric polynomial with some properties. Moreover, if the unidimenstional one is symmetric, the one so constructed is also symmetric. Finally, an example is provided.