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In this paper, we propose a new method for the construction ofmulti-dimensional, wavelet-like families of affine frames, commonly referred toas framelets, with specific directional characteristics, small and compactsupport in space, directional vanishing moments (DVM), and axial symmetries oranti-symmetries. The framelets we construct arise from readily availablerefinable functions. The filters defining these framelets have few non-zerocoefficients, custom-selected orientations and can act as finite-differenceoperators.

On the Design of Multi-Dimensional Compactly Supported Parseval Framelets with Directional Characteristics