On minimal lattice factorizations of symmetric-antisymmetric multifilterbanks

This paper introduces two minimal lattice structures for symmetric-antisymmetric multiwavelets (SAMWTs) and symmetric-antisymmetric multifilterbanks (SAMFBs). First, by exploring the relation of the symmetric-antisymmetric property in multifilterbanks and the linear-phase property in traditional scalar filterbanks, we show that the implementation and design of an SAMFB can be converted into that of a four-channel scalar linear-phase perfect reconstruction filterbank (LPPRFB). Then, based on the lattice factorization for LPPRFBs, we propose two fast, modular, minimal structures for SAMFBs. To demonstrate the effectiveness of the proposed lattice structures, several rational or dyadic-coefficient SAMWT design examples are presented along with their application in image coding.

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

[2]  Truong Q. Nguyen,et al.  A progressive transmission image coder using linear phase uniform filterbanks as block transforms , 1999, IEEE Trans. Image Process..

[3]  D. Hardin,et al.  Fractal Functions and Wavelet Expansions Based on Several Scaling Functions , 1994 .

[4]  Josef A. Nossek,et al.  Realization of multiwavelet-based transform kernels for image coding , 1998, ISCAS '98. Proceedings of the 1998 IEEE International Symposium on Circuits and Systems (Cat. No.98CH36187).

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

[6]  Truong Q. Nguyen,et al.  On M-channel linear phase FIR filter banks and application in image compression , 1997, 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.  Multirate filter banks with block sampling , 1996, IEEE Trans. Signal Process..

[9]  Kai-Kuang Ma,et al.  A simplified lattice factorization for linear-phase perfect reconstruction filter bank , 2001, IEEE Signal Process. Lett..

[10]  Xiqi Gao,et al.  Factorisation for subclass of symmetric-antisymmetric multifilter banks and its application to image coding , 2000 .

[11]  Henrique S. Malvar,et al.  The LOT: transform coding without blocking effects , 1989, IEEE Trans. Acoust. Speech Signal Process..

[12]  Xiang-Gen Xia,et al.  Vector-valued wavelets and vector filter banks , 1996, IEEE Trans. Signal Process..

[13]  Michel Barlaud,et al.  Image coding using wavelet transform , 1992, IEEE Trans. Image Process..

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

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

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

[17]  I. Daubechies,et al.  Factoring wavelet transforms into lifting steps , 1998 .

[18]  Truong Q. Nguyen,et al.  The GenLOT: generalized linear-phase lapped orthogonal transform , 1996, IEEE Trans. Signal Process..

[19]  Trac D. Tran,et al.  Lapped transform via time-domain pre- and post-filtering , 2003, IEEE Trans. Signal Process..

[20]  Truong Q. Nguyen,et al.  Linear phase paraunitary filter banks: theory, factorizations and designs , 1993, IEEE Trans. Signal Process..

[21]  Truong Q. Nguyen,et al.  On the completeness of the lattice factorization for linear-phase perfect reconstruction filter banks , 2002, IEEE Signal Processing Letters.

[22]  William A. Pearlman,et al.  A new, fast, and efficient image codec based on set partitioning in hierarchical trees , 1996, IEEE Trans. Circuits Syst. Video Technol..

[23]  Truong Q. Nguyen,et al.  On factorization of M-channel paraunitary filterbanks , 2001, IEEE Trans. Signal Process..

[24]  Michael W. Marcellin,et al.  JPEG 2000: overview, architecture, and applications , 2000, Proceedings 2000 International Conference on Image Processing (Cat. No.00CH37101).

[25]  L. Montefusco,et al.  Multiwavelet analysis and signal processing , 1998 .

[26]  Qingtang Jiang,et al.  Optimal multifilter banks: design, related symmetric extension transform, and application to image compression , 1999, IEEE Trans. Signal Process..

[27]  Truong Q. Nguyen,et al.  Linear-phase perfect reconstruction filter bank: lattice structure, design, and application in image coding , 2000, IEEE Trans. Signal Process..

[28]  Truong Q. Nguyen,et al.  Linear phase paraunitary filter bank with filters of different lengths and its application in image compression , 1999, IEEE Trans. Signal Process..

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

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

[31]  Touradj Ebrahimi,et al.  The JPEG 2000 still image compression standard , 2001, IEEE Signal Process. Mag..

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

[33]  W. Sweldens.  The Lifting Scheme: A Custom - Design Construction of Biorthogonal Wavelets "Industrial Mathematics , 1996 .

[34]  Trac D. Tran,et al.  M-channel linear phase perfect reconstruction filter bank with rational coefficients , 2002 .

[35]  Amy E. Bell,et al.  New image compression techniques using multiwavelets and multiwavelet packets , 2001, IEEE Trans. Image Process..

[36]  P. Vaidyanathan.  Multirate Systems And Filter Banks , 1992 .

[37]  Lixin Shen,et al.  On a family of orthonormal scalar wavelets and related balanced multiwavelets , 2001, IEEE Trans. Signal Process..

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

[39]  Bryan Usevitch,et al.  A tutorial on modern lossy wavelet image compression: foundations of JPEG 2000 , 2001, IEEE Signal Process. Mag..