英和和英

名詞

framelet (複数形 framelets)

1. (数学) A wavelet frame.
   • 2015 July 27, Bin Han; Qingtang Jiang; Zuowei Shen; Xiaosheng Zhuang, “Symmetric Canonical Quincunx Tight Framelets with High Vanishing Moments and Smoothness [arXiv:1507.07492v1]”, in arXiv^[1]:

     Such symmetric quincunx tight framelets are associated with quincunx tight framelet filter banks ${\displaystyle \{a;b_{1},b_{2},b_{3}\}}$ having increasing orders of vanishing moments and enjoying the additional double canonical properties: ${\displaystyle b_{1}(k_{1},k_{2})=(-1)^{1+k_{1}+k_{2}}a(1-k_{1},-k_{2}),b_{3}(k_{1},k_{2})=(-1)^{1+k_{1}+k_{2}}b_{2}(1-k_{1},-k_{2}).}$ For a low-pass filter ${\displaystyle a}$ which is not a quincunx orthonormal wavelet filter, we show that a quincunx tight framelet filter bank ${\displaystyle \{a;b_{1},\ldots ,b_{L}\}}$ with ${\displaystyle b_{1}}$ taking the above canonical form must have ${\displaystyle L\geq 3}$ high-pass filters.