COMPACTLY SUPPORTED BOX-SPLINE WAVELETS

<正> A general procedure for constructing multivariate non-tensor-product wavelets that gen-erate an orthogonal decomposition of L2（R）,s≥ 1,is described and applied to yield explicitformulas for compactly supported spline-wavelets based on the multiresolution analysis ofL2（Rs）,1≤s≤3,generated by any box spline whose direction set constitutes a unimodularmatrix.In particular,when univariate cardinal B-splines are considered,the minimally sup-ported cardinal spline-wavelets of Chui and Wang are recovered.A refined computationalscheme for the orthogonalization of spaces with compactly supported wavelets is given.Arecursive approximation scheme for“truncated”decomposition sequences is developed and asharp error bound is included.A condition on the symmetry or anti-symmetry of the waveletsis applied to yield symmetric box-spline wavelets.