A general procedure for constructing multivariate non-tensor-product wavelets that gen- erate an orthogonal decomposition of L^2(R~),s≥ 1,is described and applied to yield explicit formulas for compactly supported sp...A general procedure for constructing multivariate non-tensor-product wavelets that gen- erate an orthogonal decomposition of L^2(R~),s≥ 1,is described and applied to yield explicit formulas for compactly supported spline-wavelets based on the multiresolution analysis of L^2(R^s),1≤s≤3,generated by any box spline whose direction set constitutes a unimodular matrix.In particular,when univariate cardinal B-splines are considered,the minimally sup- ported cardinal spline-wavelets of Chui and Wang are recovered.A refined computational scheme for the orthogonalization of spaces with compactly supported wavelets is given.A recursive approximation scheme for“truncated”decomposition sequences is developed and a sharp error bound is included.A condition on the symmetry or anti-symmetry of the wavelets is applied to yield symmetric box-spline wavelets.展开更多
Pascal triangles are formulated for computing the coefficients of the B-spline series representation of the compactly supported spline-wavelets with minimum support and their derivatives.It is shown that with the al- ...Pascal triangles are formulated for computing the coefficients of the B-spline series representation of the compactly supported spline-wavelets with minimum support and their derivatives.It is shown that with the al- ternating signs removed,all these sequences are totally positive.On the other hand,truncations of the recipro- cal Euler-Frobenius polynomials lead to finite sequences for orthogonal wavelet decompositions.For this pur- pose,sharp estimates are given in terms of the exact reconstruction of these approximate decomposed compo- nents.展开更多
基金①Partially supported by ARO Grant DAAL 03-90-G-0091②Partially supported by NSF Grant DMS 89-0-01345③Partially supported by NATO Grant CRG 900158.
文摘A general procedure for constructing multivariate non-tensor-product wavelets that gen- erate an orthogonal decomposition of L^2(R~),s≥ 1,is described and applied to yield explicit formulas for compactly supported spline-wavelets based on the multiresolution analysis of L^2(R^s),1≤s≤3,generated by any box spline whose direction set constitutes a unimodular matrix.In particular,when univariate cardinal B-splines are considered,the minimally sup- ported cardinal spline-wavelets of Chui and Wang are recovered.A refined computational scheme for the orthogonalization of spaces with compactly supported wavelets is given.A recursive approximation scheme for“truncated”decomposition sequences is developed and a sharp error bound is included.A condition on the symmetry or anti-symmetry of the wavelets is applied to yield symmetric box-spline wavelets.
基金Research supported by NSF Grant DMS 89-0-01345 and ARO Contract No.DAAL 03-90-G-0091.
文摘Pascal triangles are formulated for computing the coefficients of the B-spline series representation of the compactly supported spline-wavelets with minimum support and their derivatives.It is shown that with the al- ternating signs removed,all these sequences are totally positive.On the other hand,truncations of the recipro- cal Euler-Frobenius polynomials lead to finite sequences for orthogonal wavelet decompositions.For this pur- pose,sharp estimates are given in terms of the exact reconstruction of these approximate decomposed compo- nents.
