On construction of multivariate Parseval wavelet frames

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• 作者：M. Skopina ^{skopina@MS1167.spb.edu skopinam@mail.ru}
• 关键词：Wavelet frame ; Matrix dilation ; Approximation order ; Vanishing moments
• 刊名：Applied Mathematics and Computation
• 出版年：2017
• 出版时间：15 May 2017
• 年：2017
• 卷：301
• 期：Complete
• 页码：1-11
• 全文大小：440 K
• 卷排序：301

文摘

A new method for the construction of compactly supported Parseval wavelet frames in L2(Rd)L2(Rd) with any preassigned approximation order n for arbitrary matrix dilation M   is proposed. The number of wavelet functions generating a frame constructed in this way is less or equal to (d+1)|detM|−d(d+1)|detM|−d. The method is algorithmic, and the algorithm is simple to use. The number of generating wavelet functions can be reduced to |detM||detM| for a large class of matrices M.