PSEUDO-SPLINES, WAVELETS AND FRAMELETS

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A framelet-based image inpainting algorithm (2008, methodology): “For a given ` with reflnement mask ‡`, as shown in [19, 22 ], it is easy to construct ‡ˆ, ˆ 2 “, whenever ‡` satisfles”
Dual Wavelet Frames and Riesz Bases in Sobolev Spaces (2009, background): “It is well known ([19]) that Am(ξ ) + Am(ξ + π) = 1. Furthermore, the corresponding refinable function φm is interpolatory, i.e., it is continuous and satisfies φm(k) = δk for all k ∈ Z. It has been proved in [19] (also see [ 24 ]) that limm→∞ ν2(Am) =+ ∞. The interpolatory wavelets introduced in [2”