CAJ | 학술논문

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。
여가분소파상비，불가분소파경능포착고유신호적고빈신식，정교광가재처리고유신호시능피면예려파。위료경유효지처리고유신호，본문연구료불가분정교소파긴광가적구조，제출료일충유일유소파긴광가래구조고유불가분정교소파긴광가적방법，즉선용장량적적방법구조고유소파긴광가，연후승상일개구유일정성질적삼각다항식。여과일유소파긴광가시대칭적，용본문제출적방법구조적고유불가분적정교소파긴광가야시대칭적。최후급출료일개구조산례。
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.