In this paper, we study the finite Gabor system for oversampling schemes. A characterization of dual tight frame using discrete time Zak transform is given. Also, a method to calculate coefficients expansion in case and necessary sufficient condition existence biorthogonal pair Riesz basis l2(ZL) Further, introduce notion block sliding Fourier (BSDFT) which reduces computational complexity give...

In this paper, we study the construction of irregular shearlet systems, i.e., systems of the form SH(ψ,Λ) = {a− 4 ψ(A−1 a S−1 s (x− t)) : (a, s, t) ∈ Λ}, where ψ ∈ L(R), Λ is an arbitrary sequence in R ×R×R2, Aa is a parabolic scaling matrix and Ss a shear matrix. These systems are obtained by appropriately sampling the Continuous Shearlet Transform. We derive sufficient conditions for such a d...

A common method to compute sparse solutions in compressed sensing is based on `minimization. In this paper we consider `-minimization for arbitrary 0 < p ≤ 1. More precisely, we prove stability estimates for solutions of the analysis formulation of the `minimization problem for 0 < p ≤ 1 from noisy measurements. Furthermore, our focus lies in arbitrary frames that are not necessarily tight or P...

Purpose. The aim of the present work was to test the feasibility of the time-resolved MR-angiography (TWIST-MRA) of cervical arteries using double bolus injection. Material and Methods. TWIST-MRA with a temporal resolution of 8.4 seconds for each frame and a spatial resolution with a voxel size of 0.61 × 0.58 × 0.8 mm(3) was performed in 24 patients. A biphasic bolus injection protocol was used...

The lifting scheme has been found to be a exible method for constructing scalar wavelets with desirable properties. Here it is extended to the construction of multiwavelets. It is shown that any set of compactly supported biorthogonal multiwavelets can be obtained from the Lazy matrix lters with a nite number of lifting steps. Based on the proposed lifting scheme, multiwavelet transforms that m...

For a wavelet frame with polynomial symbols generated by an MRA with a given approximation order, we present the method for parametric description and construction of all dual analysis operators (filter banks) with the maximum number of vanishing moments whose symbols are polynomials. The similar problems related to the maximum frame approximation order and some other wavelet frame properties a...

Vector wavelet transforms for vector-valued fields can be implemented directly from multiwavelets; however, existing multiwavelets offer surprisingly poor performance for transforms in vector-valued signalprocessing applications. In this paper, the reason for this performance failure is identified, and a remedy is proposed. A multiwavelet design criterion, omnidirectional balancing, is introduc...

In applications using multiwavelets there is a necessary step of associating a given discrete signal with a function in the scaling function space V 0. This association is equivalent to including a preelter and a posttl-ter for the lterbank determined by the underlying multiwavelets. We give a construction for FIR orthogonal (paraunitary) preelters that preserve the approximation order of a giv...