Symmetric–Antisymmetric Orthonormal Multiwavelets and Related Scalar Wavelets☆☆☆

By Lixin Shen, Hwee Huat Tan, Jo Yew Tham. 2000

108 citations recorded by the source corpus.

Abstract For compactly supported symmetric–antisymmetric orthonormal multiwavelet systems with multiplicity 2, we first show that any length-2Nmultiwavelet system can be constructed from a length-(2N+1) multiwavelet system and vice versa. Then we present two explicit formulations for the construction of multiwavelet functions directly from their associated multiscaling functions. This is followed by the relationship between these multiscaling functions and the scaling functions of related orthonormal scalar wavelets. Finally, we present two methods for constructing families of symmetric–antisymmetric orthonormal multiwavelet systems via the construction of the related scalar wavelets.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Media Technology

View Paper: https://www.semanticscholar.org/paper/60d473101fa04932c6ee60bc0f04ebabd6b6d8a2

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In Computer Vision and Pattern Recognition

1. Cheng-Hsiung Lee
2. Po-Whei Huang

Citations in the corpus

• Epileptic seizure detection using multiwavelet transform based approximate entropy and artificial neural networks. (2010, background): “4, 5 and 6, respectively (for review details of GHM, CL and SA4, see Geronimo et al., 1994; Chui and Lian, 1996; Shen et al., 2000).”
• Automatic Classification for Pathological Prostate Images Based on Fractal Analysis (2009, background): “The details of defining multiwavelet-SA4, -CL, and -GHM can be found in [52]–[54].”