Sobolev characterization of solutions of dilation equations
SIAM Journal on Mathematical Analysis
Energy moments in time and frequency for two-scale difference equation solutions and wavelets
SIAM Journal on Mathematical Analysis
Multirate systems and filter banks
Multirate systems and filter banks
Wavelets and subband coding
Theory and design of two-dimensional filter banks: a review
Multidimensional Systems and Signal Processing - Special issue: multidimensional filter banks and wavelets: basic theory and cosine modulated filter banks
The lifting scheme: a construction of second generation wavelets
SIAM Journal on Mathematical Analysis
Computing the Sobolev Regularity of Refinable Functions by the Arnoldi Method
SIAM Journal on Matrix Analysis and Applications
A new class of two-channel biorthogonal filter banks and waveletbases
IEEE Transactions on Signal Processing
Nonseparable two- and three-dimensional wavelets
IEEE Transactions on Signal Processing
Frame-theoretic analysis of oversampled filter banks
IEEE Transactions on Signal Processing
Biorthogonal filterbanks and energy preservation property in image compression
IEEE Transactions on Image Processing
Wavelet families of increasing order in arbitrary dimensions
IEEE Transactions on Image Processing
A New Family of Nonredundant Transforms Using Hybrid Wavelets and Directional Filter Banks
IEEE Transactions on Image Processing
Hi-index | 35.68 |
We propose structural multidimensional multichannel filter banks with desirable numbers of vanishing moments for the analysis and synthesis banks. For a two-channel filter bank, we use a three-step lifting scheme as opposed to the conventional two-step lifting method in order to provide more symmetry between the analysis and synthesis filters.We show that the resulting filters have more regularity, lower frame bounds ratio, and better frequency selectivity. We also extend our design to a general multichannel framework. Three steps of lifting scheme provides us a degree of freedom which we can benefit from toward a more flexible design.