On Compactly Supported Spline Wavelets and a Duality Principle
نویسندگان
چکیده
Let • • • C K_ ] c Vq c Vx c • • • be a multiresolution analysis of L2 generated by the mth order 5-spline Nm{x). In this paper, we exhibit a compactly supported basic wavelet i//m(x) that generates the corresponding orthogonal complementary wavelet subspaces .quently, the two finite sequences that describe the two-scale relations of Nm(x) and i//m(x) in terms of Nm(2x-j), ;6Z, yield an efficient reconstruction algorithm. To give an efficient wavelet decomposition algorithm based on these two finite sequences, we derive a duality principle, which also happens to yield the dual bases {Nm(x-j)} and {y/m(x-j)} , relative to {Nm(x-j)} and {y/m(x-j)}, respectively.
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