Orthogonal multiwavelets with vanishing moments

Gilbert Strang; Vasily Strela

doi:10.1117/12.170013

15 March 1994 Orthogonal multiwavelets with vanishing moments

Gilbert Strang, Vasily Strela

Proceedings Volume 2242, Wavelet Applications; (1994) https://doi.org/10.1117/12.170013
Event: SPIE's International Symposium on Optical Engineering and Photonics in Aerospace Sensing, 1994, Orlando, FL, United States

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. Those 'multiwavelets' open new possibilities. They can be shorter, with more vanishing moments, than single wavelets. 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", Proc. SPIE 2242, Wavelet Applications, (15 March 1994); https://doi.org/10.1117/12.170013

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