Some smooth compactly supported tight framelets associated to the quincunx matrix

详细信息    查看全文

• 作者：A. San Antol&iacute ; n^a ; ¹ ; ^{angel.sanantolin@ua.es" class="auth_mail" title="E-mail the corresponding author} ; R.A. Zalik^b ; ^{zalik@auburn.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Quincunx matrix ; Fourier transform ; Refinable function ; Tight framelet ; Unitary Extension Principle ; Vanishing moments
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 May 2016
• 年：2016
• 卷：437
• 期：1
• 页码：35-50
• 全文大小：388 K

文摘

We construct several families of tight wavelet frames in L²(R²)$L^2({\mathbb{R}}^2)$ associated to the quincunx matrix. A couple of those families has five generators. Moreover, we construct a family of tight wavelet frames with three generators. Finally, we show families with only two generators. The generators have compact support, any given degree of regularity, and any fixed number of vanishing moments. Our construction is made in Fourier space and involves some refinable functions, the Oblique Extension Principle and a slight generalization of a theorem of Lai and Stöckler. In addition, we will use well known results on construction of tight wavelet frames with two generators on R$\mathbb{R}$ with the dyadic dilation. The refinable functions we use are constructed from the Daubechies low pass filters and are compactly supported. The main difference between these families is that while the refinable functions associated to the five generators have many symmetries, the refinable functions used in the construction of the others families are merely even.