Related papers: Constructing Tight Gabor Frames Using CAZAC Sequen…

We consider the compressive sensing of a sparse or compressible signal ${\bf x} \in {\mathbb R}^M$. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce…

In this paper we introduce and investigate the concept of repro- ducing pairs as a generalization of continuous frames. Reproducing pairs yield a bounded analysis and synthesis process while the frame condition can be omitted at both…

Compressed sensing investigates the recovery of sparse signals from linear measurements. But often, in a wide range of applications, one is given only the absolute values (squared) of the linear measurements. Recovering such signals (not…

We review the Dirac formalism for dealing with constraints in a canonical Hamiltonian formulation and discuss gauge freedom and display constraints for gauge theories in a general context. We introduce the Dirac bracket and show that it…

Approximately dual frames as a generalization of duality notion in Hilbert spaces have applications in Gabor systems, wavelets, coorbit theory and sensor modeling. In recent years, the computing of the associated deviations of the canonical…

This paper investigates the properties of continuous frames, with a particular focus on phase retrieval and norm retrieval in the context of Hilbert spaces. We introduce the concept of continuous near-Riesz bases and prove their invariance…

In this paper we investigate the computational aspects of some recently proposed iterative methods for approximating the canonical tight and canonical dual window of a Gabor frame (g,a,b). The iterations start with the window g while the…

The G/G WZW model results from the WZW-model by a standard procedure of gauging. G/G WZW models are members of Dirac sigma models, which also contain twisted Poisson sigma models as other examples. We show how the general class of Dirac…

In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly…

Thermally activated delayed fluorescence (TADF) is a promising route towards high-efficiency, metal-free organic light-emitting diodes (OLEDs). However, the characterization of TADF kinetics in solid-state thin films is often complicated by…

Laser gyroscopes making use of the Sagnac effect have been used as highly accurate rotation sensors for many years. First used in aerospace and defense applications, these devices have more recently been used for precision seismology and in…

Many emerging applications involve sparse signals, and their processing is a subject of active research. We desire a large class of sensing matrices which allow the user to discern important properties of the measured sparse signal. Of…

We investigate the theory of affine groups in the context of designing radar waveforms that obey the desired wideband ambiguity function (WAF). The WAF is obtained by correlating the signal with its time-dilated, Doppler-shifted, and…

First we show that tight nonorthogonal fusion frames a relatively easy to com by. In order to do this we need to establish a classification of how to to wire a self adjoint operator as a product of (nonorthogonal) projection operators. We…

This article gives a procedure to convert a frame which is not a tight frame into a Parseval frame for the same space, with the requirement that each element in the resulting Parseval frame can be explicitly written as a linear combination…

We investigate finite sections of Gabor frames and study the asymptotic behavior of their lower Riesz bound. From a numerical point of view, these sets of time-frequency shifts are linearly dependent, whereas from a rigorous analytic point…

Gravitational-wave astronomy seeks to extract information about astrophysical systems from the gravitational-wave signals they emit. For coalescing compact-binary sources this requires accurate model templates for the inspiral and,…

We identify a class of continuous compactly supported functions for which the known part of the Gabor frame set can be extended. At least for functions with support on an interval of length two, the curve determining the set touches the…

Due to their unique ability to maintain an intensity distribution upon propagation, non-diffracting light fields are used extensively in various areas of science, including optical tweezers, nonlinear optics and quantum optics, in…

We study the optical properties of gapped graphene in presence of a magnetic field. We consider a model based on the Dirac equation, with a gap introduced via a mass term, for which analytical expressions for the diagonal and Hall optical…