For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L(R), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions which are smooth away from singularities along k-planes in R. We also develop tools to help decide whether in fact k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tigh...

For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L (R), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions which are smooth away from singularities along k-planes in R. We also develop tools to help decide whether in fact k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tig...

We study Weyl-Heisenberg (=Gabor) expansions for either L2(IR ) or a subspace of it. These are expansions in terms of the spanning set X = (EM φ : k ∈ K, l ∈ L,φ ∈ Φ), where K and L are some discrete lattices in IR, Φ ⊂ L2(IR ) is finite, E is the translation operator, and M is the modulation operator. Such sets X are known as WH systems. The analysis of the “basis” properties of WH systems (e....

We study Weyl-Heisenberg (=Gabor) expansions for either L 2 (IR d) or a subspace of it. These are expansions in terms of the spanning set where K and L are some discrete lattices in IR d , L 2 (IR d) is nite, E is the translation operator, and M is the modulation operator. Such sets X are known as WH systems. The analysis of the \basis" properties of WH systems (e.g. being a frame or a Riesz ba...

We introduce the concept of the modular function for a shiftinvariant subspace that can be represented by normalized tight frame generators for the shift-invariant subspace and prove that it is independent of the selections of the frame generators for the subspace. We shall apply it to study the connections between the dimension functions of wavelet frames for any expansive integer matrix A and...

If the wavelet system {aψ(a ·−bk)}j,k∈Z forms a frame onL(R) for some a > 1 and b > 0, then it is called a (regular) wavelet frame. In this case we can reconstruct any f from the sampled values (Wψf)(a , abk). In practice the sampling points may be irregular. We need to know for which wavelet ψ and parameters {(sj , bk)}j,k , the wavelet system {s j ψ(sj · −bk)}j,k∈Z forms a frame on L (R). In ...

Let {xn} be a frame for a Hilbert space H. We investigate the conditions under which there exists a dual frame for {xn} which is also a Parseval (or tight) frame. We show that the existence of a Parseval dual is equivalent to the problem whether {xn} can be dilated to an orthonormal basis (under an oblique projection). A necessary and sufficient condition for the existence of Parseval duals is ...

DA strain and other members of the TO subgroup of Theiler's murine encephalomyelitis virus (TMEV) produce a chronic demyelinating disease in which the virus persists but has a restricted expression. We previously reported that TO subgroup strains, in addition to synthesizing the picornaviral polyprotein, use an alternative initiation codon just downstream from the polyprotein's AUG to translate...

This article gives results on fixed basis frame valued neighborhood topological groups and stratified neighborhood topological groups, includes some characterization theorems, and presents the uniformizability of stratified neighborhood topological groups within the unified approach of Gutiérrez García, DePrada Vicente, and Šostak. It is shown that for a frame L, the category L-NGrp is topologi...