Related papers: A note on Gabor frames in finite dimensions
Adaptive dimensionality reduction in high-dimensional problems is a key topic in statistics. The multiplicative gamma process takes a relevant step in this direction, but improved studies on its properties are required to ease…
Phase retrieval arises in various fields of science and engineering and it is well studied in a finite-dimensional setting. In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-valued signals living…
The ability to resolve detail in the object that is being imaged, named by resolution, is the core parameter of an imaging system. Super-resolution is a class of techniques that can enhance the resolution of an imaging system and even…
This survey offers a systematic and streamlined exposition of the most important characterizations of Gabor frames over a lattice. The goal is to collect the most important characterizations of Gabor frames and offer a systematic exposition…
This paper continues a study of field theories specified for the nonuniform lattice in the finite-dimensional hypercube with the use of the earlier described deformation parameters. The paper is devoted to spontaneous breakdown and…
A general principle says that the matrix of a Fourier integral operator with respect to wave packets is concentrated near the curve of propagation. We prove a precise version of this principle for Fourier integral operators with a smooth…
We consider a class of systems over finite alphabets with linear internal dynamics, finite-valued control inputs and finitely quantized outputs. We motivate the need for a new notion of observability and propose three new notions of output…
The decomposition of multiport interferometers is a fundamental tool in quantum optics and computing. This note aims to serve as a concise reference for performing the decomposition according to the most common design approaches, offering a…
Texture analysis and classification remain as one of the biggest challenges for the field of computer vision and pattern recognition. On this matter, Gabor wavelets has proven to be a useful technique to characterize distinctive texture…
Future radar systems are expected to use waveforms of a high bandwidth, where the main advantage is an improved range resolution. In this paper, a technique to design robust wideband waveforms for a Multiple-Input-Single-Output system is…
Consider a scenario in which an unknown signal is transformed by a known linear operator, and then the pointwise absolute value of the unknown output function is reported. This scenario appears in several applications, and the goal is to…
We present a time-frequency framework adapted to dispersive phase functions via a subdyadic geometry in phase space. On top of this geometry we construct stable Gabor frames with quantitative control of overlap, almost orthogonality, and…
We study finite systems of vectors whose frame operator matrices are unitarily equivalent, via explicit and computationally efficient unitary transformations, to block-diagonal matrices. We call such systems block-equivalent. We show that a…
We construct and justify leading order weakly nonlinear geometric optics expansions for nonlinear hyperbolic initial value problems, including the compressible Euler equations. The technique of simultaneous Picard iteration is employed to…
The aim of this note is to provide a natural extension of Gelfond's constant $e^\pi$ using a hypergeometric function approach. An extension is also found for the square root of this constant. A few interesting special cases are presented.
We study the phase reconstruction of signals $f$ belonging to complex Gaussian shift-invariant spaces $V^\infty(\varphi)$ from spectrogram measurements $|\mathcal{G} f(X)|$ where $\mathcal{G}$ is the Gabor transform and $X \subseteq…
We consider frames in a finite-dimensional Hilbert space Hn where frames are exactly the spanning sets of the vector space. We present a method to determine the maximum robustness of a frame. We present results on tight subframes and…
This is an attempt of a comprehensive survey of the results in which estimates of the norms of linear means of multiple Fourier series, the Lebesgue constants, are obtained by means of estimating the Fourier transform of a function…
G-frames are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural…
In this work we study families of pairs of window functions and lattices which lead to Gabor frames which all possess the same frame bounds. To be more precise, for every generalized Gaussian $g$, we will construct an uncountable family of…