framelet

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)a(1-k_1,-k_2),b_3(k_1,k_2)=(-1)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,…,b_L with b_1 taking the above canonical form must have L>3 high-pass filters.