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Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method

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Construction of arbitrary dimensional biorthogonal multiwavelet using lifting scheme.

Xieping Gao¹, Fen Xiao, Bodong Li

¹College of Information Engineering and Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, China.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|April 4, 2009

Summary

This summary is machine-generated.

This study introduces a novel framework for constructing multidimensional biorthogonal multiwavelets and filter banks using a generalized lifting scheme. These advanced multiwavelet systems offer efficient computation and preserve key properties for diverse applications.

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Area of Science:

Signal Processing
Applied Mathematics
Numerical Analysis

Background:

Multidimensional signal processing often requires sophisticated wavelet transforms.
Existing methods may lack flexibility in terms of dimensionality and vanishing moments.

Purpose of the Study:

To develop a general design framework for multidimensional biorthogonal multiwavelets.
To construct perfect reconstruction multifilter banks based on the Hermite-Neville filter.

Main Methods:

Utilizing two lifting structures derived from the Hermite-Neville filter.
Developing a generalized lifting scheme for multiwavelet construction.
Investigating properties like multiplicity, lattice, dimension, and vanishing moments.

Main Results:

A general framework for constructing biorthogonal multiwavelets and Hermite interpolation filter banks.
The construction generalizes the Neville-based lifting scheme.
The proposed systems inherit advantages of lifting schemes: fast computation, in-place, and integer-to-integer transforms.

Conclusions:

The developed multiwavelet systems offer significant advantages for signal processing applications.
These systems preserve desirable properties such as interpolation, short support, symmetry, and high vanishing moments.