framelet

English

Etymology

frame +‎ -let

Noun

framelet (plural framelets)

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