Related papers: Frames adapted to a phase-space cover
The purpose of this note is to present a proof of the existence of Gabor frames in general linear position in all finite dimensions. The tools developed in this note are also helpful towards an explicit construction of such a frame, which…
Optical beams and starlight distorted by atmospheric turbulence can be corrected with adaptive optics systems to enable efficient coupling into single-mode fibers. Deformable mirrors, used to flatten the wavefront in astronomical…
Meeting the high data rate demands of modern applications necessitates the utilization of high-frequency spectrum bands, including millimeter-wave and sub-terahertz bands. However, these frequencies require precise alignment of narrow…
Video frame interpolation, the synthesis of novel views in time, is an increasingly popular research direction with many new papers further advancing the state of the art. But as each new method comes with a host of variables that affect…
Interferometry provides highly sensitive access to optical phase and is central to much of modern metrology and phase imaging methods. Conventional implementations, however, often face trade-offs between mechanical stability and…
We present the applications of wavelet analysis methods in constrained variational framework to calculation of dynamical aperture. We construct represention via exact nonlinear high-localized periodic eigenmodes expansions, which allows to…
A family of Parseval periodic wavelet frames is constructed. The family has optimal time-frequency localization (in the sense of the Breitenberger uncertainty constant) with respect to a family parameter and it has the best currently known…
We present two spatial-shaping approaches -- phase and amplitude -- for creating two-dimensional optical dipole potentials for ultracold neutral atoms. When combined with an attractive or repulsive Gaussian sheet formed by an astigmatically…
In recent times, we experimentally realized a quite efficient modeling of the shape of diffraction-resistant optical beams; thus generating for the first time the so-called Frozen Waves (FW), whose longitudinal intensity pattern can be…
Time-frequency analysis, such as the Gabor transform, plays an important role in many signal processing applications. The redundancy of such representations is often directly related to the computational load of any algorithm operating in…
Adapting image-pretrained backbones to video typically relies on time-domain adapters tuned to a single temporal scale. Our experiments show that these modules pick up static image cues and very fast flicker changes, while overlooking…
The quantum mechanical harmonic oscillator Hamiltonian generates a one-parameter unitary group W(\theta) in L^2(R) which rotates the time-frequency plane. In particular, W(\pi/2) is the Fourier transform. When W(\theta) is applied to any…
This work developes a quantitative framework for describing the overcompleteness of a large class of frames. A previous paper introduced notions of localization and approximation between two frames $\mathcal{F} = \{f_i\}_{i \in I}$ and…
We address the problem of signal reconstruction from intensity measurements with respect to a measurement frame. This non-convex inverse problem is known as phase retrieval. The case considered in this paper concerns phaseless measurements…
We describe a random matrix approach that can provide generic and readily soluble mean-field descriptions of the phase diagram for a variety of systems ranging from QCD to high-T_c materials. Instead of working from specific models, phase…
We introduce, and propagate wave-packet solutions of, a single qubit system in which geometric gauge forces and phases emerge. We investigate under what conditions non-trivial gauge phenomena arise, and demonstrate how symmetry breaking is…
Nonstationary Gabor frames, recently introduced in adaptive signal analysis, represent a natural generalization of classical Gabor frames by allowing for adaptivity of windows and lattice in either time or frequency. Due to the lack of a…
Perhaps the simplest approach to constructing models with sub-dimensional particles or fractons is to require the conservation of dipole or higher multipole moments. We generalize this approach to allow for moments in phase space and…
We investigate Gabor frames on locally compact abelian groups with time-frequency shifts along non-separable, closed subgroups of the phase space. Density theorems in Gabor analysis state necessary conditions for a Gabor system to be a…
Tight frames can be characterized as those frames which possess optimal numerical stability properties. In this paper, we consider the question of modifying a general frame to generate a tight frame by rescaling its frame vectors; a process…