Let ... subset-of V-1 subset-of V0 subset-of V1 subset-of ... be a multiresolution analysis of L2 generated by the mth order B-spline Nm(x). In this paper, we exhibit a compactly supported basic wavelet psi(m)(x) that generates the corresponding or-thogonal complementary wavelet subspaces ..., W-1, W0, W1, .... Consequently, the two finite sequences that describe the two-scale relations of Nm(x) and psi(m)(x) in terms of N(m) (2x - j), j is-an-element-of Z, 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 {N(m) approximately (x - j)} and {psi(m) approximately (x - j)}, relative to {N(m)(x - j)} and {psi(m)(x - j)}, respectively.
