Abstract
Let n be an integer and c be an integer or a semi-integer. For an arbitrary matrix dilation, we describe all masks that are symmetric with respect to the point c and have sum rule of order n. For each such mask, we give explicit formulas for the wavelet masks that are point symmetric/antisymmetric and generate a frame-like wavelet system providing approximation order n. For any matrix dilation (that is appropriate for the axial symmetry group on Zd in some natural sense), axial symmetric/antisymmetric frame-like wavelet systems providing approximation order n are constructed. Also, for several matrix dilations, the explicit construction of highly symmetric frame-like wavelet systems providing approximation order n is presented.
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