We consider a generator F 1⁄4 ðf1; y ;fNÞ for either a multi-frame or a super-frame generated under the action of a projective unitary representation for a discrete countable group. Examples of such frames include Gabor multi-frames, Gabor super-frames and frames for shift-invariant subspaces. We show that there exists a unique normalized tight multi-frame (resp. super-frame) generator C 1⁄4 ðc...

Let H be a separable Hilbert space, let G ⊂ H, and let A be an operator on H. Under appropriate conditions on A andG, it is known that the set of iterations FG(A) = {Ag | g ∈ G, 0 ≤ j ≤ L(g)} is a frame for H. We call FG(A) a dynamical frame for H, and explore further its properties; in particular, we show that the canonical dual frame of FG(A) also has an iterative set structure. We explore th...

Multiple attributes of a single-object are often processed more easily than attributes of different objects-a phenomenon associated with object attention. Here we investigate the influence of two factors, judgment frames and judgment precision, on dual-object report deficits as an index of object attention. [Han, S., Dosher, B., & Lu, Z.-L. (2003). Object attention revisited: Identifying mechan...

The present paper for the first time constructs a frame/dual frame pair of shearlet type such that both frames possess the distinctive time-frequency localization properties needed in establishing their desirable approximation properties. Our construction is based on a careful pasting together of two bandlimited shearlet Parseval frames associated with two different frequency cones, inspired by...

A 1 bp Deletion in the Dual Reading Frame Deafness Gene LRTOMT Causes a Frameshift From the First Into the Second Reading Frame Maarten Vanwesemael, Isabelle Schrauwen, Ruben Ceuppens, Fatemeh Alasti, Ellen Jorssen, Effat Farrokhi, Morteza Hashemzadeh Chaleshtori, and Guy Van Camp* Department of Medical Genetics, University of Antwerp, 2610, Wilrijk, Belgium Cellular and Molecular Research Cent...

We study the Laplacian pyramid (LP) as a frame operator, and this reveals that the usual reconstruction is suboptimal. With orthogonal filters, the LP is shown to be a tight frame, thus the optimal linear reconstruction using the dual frame operator has a simple structure as symmetrical with the forward transform. For more general cases, we propose an efficient filter bank for reconstruction in...

In this paper we show that any shift-invariant Bessel sequence with an at most countable number of generators can be extended to a tight frame for its closed linear span by adding another shift-invariant system with at most the same number of generators. We show that in general this result is optimal, by providing examples where it is impossible to obtain a tight frame by adding a smaller numbe...

An explicit method for the construction of a tight wavelet frame generated by the Walsh polynomials with the help of extension principles was presented by Shah (Shah, 2013). In this article, we extend the notion of wavelet frames to periodic wavelet frames generated by the Walsh polynomials on R by using extension principles. We first show that under some mild conditions, the periodization of a...

Abstract. A Weyl-Heisenberg frame for L(R) is a frame consisting of translates and modulates of a fixed function in L(R), i.e. (EmbTnag)m,n∈Z , with a, b > 0, and g ∈ L(R). In this paper we will give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions g so that (EmbTnag) is an orthonormal basis for L (R). These resu...