  In this paper, we propose a new method for the construction of
multi-dimensional, wavelet-like families of affine frames, commonly referred to
as framelets, with specific directional characteristics, small and compact
support in space, directional vanishing moments (DVM), and axial symmetries or
anti-symmetries. The framelets we construct arise from readily available
refinable functions. The filters defining these framelets have few non-zero
coefficients, custom-selected orientations and can act as finite-difference
operators.
