Ten lectures on wavelets
Multirate systems and filter banks
Multirate systems and filter banks
An interior algorithm for nonlinear optimization that combines line search and trust region steps
Mathematical Programming: Series A and B
Watermarking via zero assigned filter banks
Signal Processing
Design of orthonormal Hilbert-pair of wavelets using zero-pinning
Signal Processing
Image denoising with anisotropic bivariate shrinkage
Signal Processing
Symmetric self-Hilbertian filters via extended zero-pinning
Signal Processing
The design of approximate Hilbert transform pairs of wavelet bases
IEEE Transactions on Signal Processing
A Novel Scheme for the Design of Approximate Hilbert Transform Pairs of Orthonormal Wavelet Bases
IEEE Transactions on Signal Processing
Hilbert Pair of Orthogonal Wavelet Bases: Revisiting the Condition
IEEE Transactions on Signal Processing
SDP Approximation of a Fractional Delay and the Design of Dual-Tree Complex Wavelet Transform
IEEE Transactions on Signal Processing
Image quality assessment: from error visibility to structural similarity
IEEE Transactions on Image Processing
Sharper Symmetric Self-Hilbertian wavelets
Signal Processing
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The dual-tree complex wavelet transform offers near shift invariance and a better directional selectivity compared to traditional discrete wavelet transforms. A new class of Hilbert-pair of wavelets that can be used in the dual-tree is presented in this work. These Hilbert-pairs are exactly orthogonal but are also almost symmetric. They therefore have the advantages found in both orthogonal and biorthogonal wavelets. Symmetry in the wavelets is of prime importance in many applications as it offers a better directional selectivity. An efficient and flexible design technique is proposed for the design of these new Hilbert-pairs. The proposed technique readily allows the designer to trade-off between the degree of symmetry and the analytic quality. The designed wavelet filters have good frequency response, flat group delay and achieve a good approximation to the half-sample delay condition which is required for good analytic quality.