Constructing Pairs of Dual Bandlimited Frame Wavelets in L(r)

Constructing pairs of dual bandlimited frame wavelets in L^2(R^n)

Given a real, expansive dilation matrix we prove that any bandlimited function ψ ∈ L(R), for which the dilations of its Fourier transform form a partition of unity, generates a wavelet frame for certain translation lattices. Moreover, there exists a dual wavelet frame generated by a finite linear combination of dilations of ψ with explicitly given coefficients. The result allows a simple constr...

Constructing pairs of dual bandlimited framelets with desired time localization

G-dual function-valued frames in L2(0,∞)

In this paper, g-dual function-valued frames in L2(0;1) are in- troduced. We can achieve more reconstruction formulas to ob- tain signals in L2(0;1) by applying g-dual function-valued frames in L2(0;1).

Pairs of Dual Wavelet Frames from Any Two Refinable Functions

Starting from any two compactly supported refinable functions in L2(R) with dilation factor d, we show that it is always possible to construct 2d wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L2(R). Moreover, the number of vanishing moments of each of these wavelet frames is equal to the approximation order of the dual MRA; this is the highest...

On dual shearlet frames

In This paper, we give a necessary condition for function in $L^2$ with its dual to generate a dual shearlet tight frame with respect to admissibility.