A linear programming approach to solving bilinear programmes
Mathematical Programming: Series A and B
The Translation Sensitivity of Wavelet-Based Registration
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convex Optimization
Robust Face Recognition via Sparse Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Signal Processing - Part II
The design of approximate Hilbert transform pairs of wavelet bases
IEEE Transactions on Signal Processing
Optimal design of complex FIR filters with arbitrary magnitude and group delay responses
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
SDP Approximation of a Fractional Delay and the Design of Dual-Tree Complex Wavelet Transform
IEEE Transactions on Signal Processing
Symmetric self-Hilbertian filters via extended zero-pinning
Signal Processing
A new class of almost symmetric orthogonal Hilbert pair of wavelets
Signal Processing
Sharper Symmetric Self-Hilbertian wavelets
Signal Processing
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It is understood that the Hilbert transform pairs of orthonormal wavelet bases can only be realized approximately by the scaling filters of conjugate quadrature filter (CQF) banks. In this paper, the approximate FIR realization of the Hilbert transform pairs is formulated as an optimization problem in the sense of the lp (p = 1, 2, or infinite) norm minimization on the approximate error of the magnitude and phase conditions of the scaling filters.The orthogonality and regularity conditions of the CQF bank pairs are taken as the constraints of such an optimization problem.Whereafter the branch and bound technique is employed to obtain the globally optimal solution of the resulting bilinear program optimization problem. Since the orthogonality and regularity conditions are explicitly taken as the constraints of our optimization problem, the attained solution is an approximate Hilbert transform pair satisfying these conditions exactly. Some orthogonal wavelet bases designed herein demonstrate that our design scheme is superior to those that have been reported in the literature. Moreover,the designed orthogonal wavelet bases show that minimizing the l1norm of the approximate error should be advocated for obtaining better approximated Hilbert pairs.