Orthogonal multiwavelets with vanishing moments

Gilbert Strang; Vasily Strela

doi:10.1117/12.172247

1 July 1994 Orthogonal multiwavelets with vanishing moments

Gilbert Strang, Vasily Strela

Author Affiliations +

Optical Engineering, Vol. 33, Issue 7, (July 1994). https://doi.org/10.1117/12.172247

Abstract

A scaling function is the solution to a dilation equation Φ(t) = Σc_kΦ(2t - k), in which the coefficients come from a low-pass filter. The coefficients in the wavelet W(t) = Σd_kΦ(2t - k) come from a high-pass filter. When these coefficients are matrices, Φ and W are vectors: there are two or more scaling functions and an equal number of wavelets. By dilation and translation of the wavelets, we have an orthogonal basis W_ijk = W_i(2^jt - k) for all functions of finite energy. These "multiwavelets" open new possibilities. They can be shorter, with more vanishing moments, than single wavelets. They can be symmetric, which is impossible for scalar wavelets (except for Haar's). We determine the conditions to impose on the matrix coefficients c_k in the design of multiwavelets, and we construct a new pair of piecewise linear orthogonal wavelets with two vanishing moments.

Citation Download Citation

Gilbert Strang and Vasily Strela "Orthogonal multiwavelets with vanishing moments," Optical Engineering 33(7), (1 July 1994). https://doi.org/10.1117/12.172247

Published: 1 July 1994

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