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...

In this paper we shall characterize Sobolev spaces of an arbitrary order of smoothness using nonstationary tight wavelet frames for L2(R). In particular, we show that a Sobolev space of an arbitrary fixed order of smoothness can be characterized in terms of the weighted `2-norm of the analysis wavelet coefficient sequences using a fixed compactly supported nonstationary tight wavelet frame in L...

‎we study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎these equations will be converted to a system of‎ ‎singular integral equations with cauchy type kernels‎. ‎using‎ ‎chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of cauchy type singular integral equation which will ...

This paper proposes a novel method for synchronizing high frame-rate (HFR) camera with an HFR projector, using visual feedback-based synchronization algorithm streaming video sequences in real time on visible-light communication (VLC)-based system. The frame rates of the and projector are equal, their phases synchronized. A is used to mitigate complexities stabilization issues wire-based trigge...

In J. T. Wilson’s doctoral dissertation, the author takes up the subject of free meets, that is, subsets S of a frame L whose meet V S is preserved by a designated class of frame homomorphisms out of L. Wilson proves that all subsets of L have free meets if and only if the dual frame law holds in L and the assembly NL is a boolean frame. In this paper it is shown that a frame L has free meets w...

In this paper we propose a method for automatic local time adaptation of the spectrogram of an audio signal, based on its decomposition within a Gabor multi-frame. The sparsity of the analyses within each individual frame is evaluated through the Rényi entropies measures. According to the sparsity of the decompositions, an optimal resolution and a reduced multi-frame are determined, defining an...

Several concepts for the localization of a frame are studied. The intrinsic localization of a frame is defined by the decay properties of its Gramian matrix. Our main result asserts that the canonical dual frame possesses the same intrinsic localization as the original frame. The proof relies heavily on Banach algebra techniques, in particular on recent spectral invariance properties for certai...

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...

This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames F = {f i } i∈I and E = {e j } j∈G (G a discrete abelian group), relating the decay of the expansion of the elements of F in terms of the elements of E via a map a : I → G. A fundamental set of equalities are shown ...

PURPOSE The hyperpolarized gases (3)He and (129)Xe have distinct properties and provide unique and complementary functional information from the lungs. A triple-nuclear, same-breath imaging examination of the lungs with (1)H, (3)He, and (129)Xe can therefore provide exclusive functional information from the gas images. In addition, the (1)H images provide complementary co-registered structural ...