Biorthogonal nonuniform B-spline wavelets based on a discrete norm

This paper utilizes a recursive formula for transformation matrices of B-spline bases to construct biorthogonal nonuniform B-spline wavelets based on discrete norm l2 and proposes the reconstruction and decomposition algorithms for the MRA of the wavelets. The computation of reconstruction matrices of the proposed wavelets is based on simple recursion and integral operation is avoided. The reconstruction and decomposition algorithms are both simple, efficient and with linear time complexity. Moreover, the analysis for the performances of the proposed wavelets reveals that the wavelets possess smaller supports in general cases compared with that of semiorthogonal nonuniform B-spline wavelets, with good approximation property and suitable for any uniform and nonuniform nested sequences of knot vectors. Several examples are given for the applications of the proposed wavelets in the MRA of nonuniform B-spline curves. The experimental results show that as any other nonuniform B-spline wavelets, the proposed wavelets provide greater flexibility than uniform B-spline wavelets do for the applications of the MRA of B-spline curves and surfaces. With the proposed wavelets we can easily construct rich multiresolution levels and maintain the specified characteristic points as well as local details of the decomposed curves to satisfy various requirements in the applications.