We analyse the relation between innnite-dimensional frame theory and nite-dimensional models for frames as they are used for numerical algorithms. Special emphasis in this paper is on perfect reconstruction oversampled lter banks, also known as shift-invariant frames. For certain nite-dimensional models it is shown that the corresponding nite dual frame provides indeed an approximation of the d...

An interesting method called Oblique Extension Principle (OEP) has been proposed in the literature for constructing compactly supported MRA tight and dual wavelet frames with high vanishing moments and high frame approximation orders. Many compactly supported MRA wavelet frames have been recently constructed from scalar refinable functions via OEP. Despite the great flexibility and popularity o...

In this paper we consider  (extended) metaplectic representation of the  semidirect product  $G_{mathbb{J}}=mathbb{R}^{2d}timesmathbb{J}$  where $mathbb{J}$ is a closed subgroup of $Sp(d,mathbb{R})$, the symplectic group. We will investigate continuous representation frame on $G_{mathbb{J}}$. We also discuss the existence of duals for such frames and give several characterization for them. Fina...

in this paper, we first discuss about canonical dual of g-frameλp = {λip ∈ b(h, hi) : i ∈ i}, where λ = {λi ∈ b(h, hi) :i ∈ i} is a g-frame for a hilbert space h and p is the orthogonalprojection from h onto a closed subspace m. next, we provethat, if λ = {λi ∈ b(h, hi) : i ∈ i} and θ = {θi ∈ b(k, hi) :i ∈ i} be respective g-frames for non zero hilbert spaces hand k, and λ and θ are unitarily e...

In order to obtain better coverage of the population of interest and cost less, a number of surveys employ dual frame structure, in which independent samples are taken from two overlapping sampling frames. This research considers chi-squared tests in dual frame surveys when categorical data is encountered. We extend generalized Wald’s (1943) test, Rao-Scott first-order and second-order correcte...

In [1], Savage described a unified mathematical framework for strapdown inertial navigation algorithm design. The commenting note [2] showed that the " velocity translation vector " (VTV) in the Savage's framework is equivalent to the dual part of an appropriate screw vector in the dual quaternion representation [3] and significantly simplified the VTV rate equation by way of the screw vector r...

OBJECTIVE Right-angle dual-headed tomography has increased cardiac SPECT utility by cutting acquisition time in half which enhances gating capabilities. When gating, however, a deceleration in heart rate, due to a return to baseline rate after stress or lessened anxiety at the end of a study, may significantly affect the last step(s) of a gated study with possible frame or information loss. The...

We construct non-tight frames in finite-dimensional spaces consisting of periodic functions. In order for these frames to be useful in practice one needs to calculate a dual frame; while the canonical dual frame might be cumbersome to work with, the setup presented here enables us to obtain explicit constructions of some particularly convenient oblique duals. We also provide explicit oblique du...