On a family of orthonormal scalar wavelets and related balanced multiwavelets

For a family of length-4N orthonormal scalar wavelet filters that has been shown to be closely related to symmetric/antisymmetric orthonormal multifilters (SAOMFs), a sufficient and necessary condition is given for their construction. A near-linear criterion is then provided for constructing balanced multiwavelet filters related to these scalar filters. Numerical results are presented to demonstrate the potential usefulness of this criterion.

[1]  Ivan W. Selesnick,et al.  Multiwavelet bases with extra approximation properties , 1998, IEEE Trans. Signal Process..

[2]  D. Hardin,et al.  Multiwavelet prefilters. 1. Orthogonal prefilters preserving approximation order p/spl les/2 , 1998 .

[3]  Akram Aldroubi,et al.  Projection based prefiltering for multiwavelet transforms , 1998, IEEE Trans. Signal Process..

[4]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[5]  C. Chui,et al.  A study of orthonormal multi-wavelets , 1996 .

[6]  Qingtang Jiang,et al.  On the design of multifilter banks and orthonormal multiwavelet bases , 1998, IEEE Trans. Signal Process..

[7]  Jo Yew Tham,et al.  Some properties of symmetric-antisymmetric orthonormal multiwavelets , 2000, IEEE Trans. Signal Process..

[8]  Xiang-Gen Xia,et al.  A new prefilter design for discrete multiwavelet transforms , 1997, Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136).

[10]  Xiang-Gen Xia,et al.  Design of prefilters for discrete multiwavelet transforms , 1996, IEEE Trans. Signal Process..

[11]  Martin Vetterli,et al.  Balanced multiwavelets theory and design , 1998, IEEE Trans. Signal Process..

[12]  Jo Yew Tham,et al.  A general approach for analysis and application of discrete multiwavelet transforms , 2000, IEEE Trans. Signal Process..

[13]  T. R. Downie,et al.  The discrete multiple wavelet transform and thresholding methods , 1998, IEEE Trans. Signal Process..

[14]  Jo Yew Tham,et al.  New biorthogonal multiwavelets for image compression , 1999, Signal Process..

[15]  Qingtang Jiang,et al.  Orthogonal multiwavelets with optimum time-frequency resolution , 1998, IEEE Trans. Signal Process..

[16]  Peter N. Heller,et al.  The application of multiwavelet filterbanks to image processing , 1999, IEEE Trans. Image Process..

[17]  Peter Rieder.  Parameterization of symmetric multiwavelets , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[18]  P. P. Vaidyanathan,et al.  Lattice structures for optimal design and robust implementation of two-channel perfect-reconstruction QMF banks , 1988, IEEE Trans. Acoust. Speech Signal Process..

[19]  Jo Yew Tham,et al.  Symmetric–Antisymmetric Orthonormal Multiwavelets and Related Scalar Wavelets☆☆☆ , 2000 .