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Related papers: Gabor fusion frames generated by difference sets

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Let $(g_{nm})_{n,m\in Z}$ be a Gabor frame for $L_2(R)$ for given window $g$. We show that the window $h^0=S^{-1/2} g$ that generates the canonically associated tight Gabor frame minimizes $\|g-h\|$ among all windows $h$ generating a…

Functional Analysis · Mathematics 2025-10-20 A. J. E. M Janssen , Thomas Strohmer

We introduce a fast algorithm for computing sparse Fourier transforms supported on smooth curves or surfaces. This problem appear naturally in several important problems in wave scattering and reflection seismology. The main observation is…

Numerical Analysis · Mathematics 2008-01-11 Lexing Ying

Understanding the macroscopic behavior of dynamical systems is an important tool to unravel transport mechanisms in complex flows. A decomposition of the state space into coherent sets is a popular way to reveal this essential macroscopic…

Dynamical Systems · Mathematics 2020-04-30 Gary Froyland , Péter Koltai , Martin Stahn

We study the dynamical behavior of a single degree of freedom mechanical system with a particle damper. The particle (granular) damping was optimized for the primary system operating condition by using an appropriate gap size for a…

Soft Condensed Matter · Physics 2013-02-19 Martín Sánchez , C. Manuel Carlevaro

This document proposes a Unified Robust Framework that re-engineers the estimation of the Average Treatment Effect on the Overlap (ATO). It synthesizes gamma-Divergence for outlier robustness, Graduated Non-Convexity (GNC) for global…

Machine Learning · Statistics 2025-11-25 Eichi Uehara

Audio signal processing frequently requires time-frequency representations and in many applications, a non-linear spacing of frequency-bands is preferable. This paper introduces a framework for efficient implementation of invertible signal…

Functional Analysis · Mathematics 2013-05-17 Nicki Holighaus , Monika Dörfler , Gino Angelo Velasco , Thomas Grill

Modeling geospatial tabular data with deep learning has become a promising alternative to traditional statistical and machine learning approaches. However, existing deep learning models often face challenges related to scalability and…

Machine Learning · Computer Science 2025-02-24 Rui Deng , Ziqi Li , Mingshu Wang

Generative graph models struggle to scale due to the need to predict the existence or type of edges between all node pairs. To address the resulting quadratic complexity, existing scalable models often impose restrictive assumptions such as…

Machine Learning · Computer Science 2024-05-24 Yiming Qin , Clement Vignac , Pascal Frossard

In this paper, we extend a famous motion planning approach GPMP2 to multi-robot cases, yielding a novel centralized trajectory generation method for the multi-robot formation. A sparse Gaussian Process model is employed to represent the…

Robotics · Computer Science 2021-08-02 Shuang Guo , Bo Liu , Shen Zhang , Jifeng Guo , Changhong Wang

The optimal properties for single photons may vary drastically between different quantum technologies. Along with central frequency conversion, control over photonic temporal waveforms will be paramount to the effective coupling of…

Quantum Physics · Physics 2015-03-10 John M. Donohue , Michael D. Mazurek , Kevin J. Resch

A Python package for the calculation of spectrograms with optimized time and frequency resolution for application in the analysis of numerical simulations on ultrashort pulse propagation is presented. Gabor's uncertainty principle prevents…

Computational Physics · Physics 2018-09-05 O. Melchert , B. Roth , U. Morgner , A. Demircan

Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only "approximately sparse", i.e. even though the signal contains only a small fraction of relevant (large)…

Information Theory · Computer Science 2013-04-04 Jean Barbier , Florent Krzakala , Marc Mézard , Lenka Zdeborová

Compressed Neural Networks have the potential to enable deep learning across new applications and smaller computational environments. However, understanding the range of learning tasks in which such models can succeed is not well studied.…

Machine Learning · Computer Science 2023-08-10 Matt Gorbett , Hossein Shirazi , Indrakshi Ray

We provide a systematic deterministic numerical scheme to approximate the volume (i.e. the Lebesgue measure) of a basic semi-algebraic set whose description follows a sparsity pattern. As in previous works (without sparsity), the underlying…

Optimization and Control · Mathematics 2020-07-28 Matteo Tacchi , Tillmann Weisser , Jean-Bernard Lasserre , Didier Henrion

We describe an approach based on compressive-sampling which allows for a considerable reduction in the acquisition time in Fourier-transform spectroscopy. In this approach, an N-point Fourier spectrum is resolved from much less than N…

Optics · Physics 2010-06-15 Ori Katz , Jonathan M. Levitt , Yaron Silberberg

In high-dimensional generalized linear models, it is crucial to identify a sparse model that adequately accounts for response variation. Although the best subset section has been widely regarded as the Holy Grail of problems of this type,…

Machine Learning · Statistics 2023-08-02 Junxian Zhu , Jin Zhu , Borui Tang , Xuanyu Chen , Hongmei Lin , Xueqin Wang

The problem of approximately computing the $k$ dominant Fourier coefficients of a vector $X$ quickly, and using few samples in time domain, is known as the Sparse Fourier Transform (sparse FFT) problem. A long line of work on the sparse FFT…

Data Structures and Algorithms · Computer Science 2017-04-12 Volkan Cevher , Michael Kapralov , Jonathan Scarlett , Amir Zandieh

Group-based sparsity models are proven instrumental in linear regression problems for recovering signals from much fewer measurements than standard compressive sensing. The main promise of these models is the recovery of "interpretable"…

Machine Learning · Computer Science 2015-03-05 Luca Baldassarre , Nirav Bhan , Volkan Cevher , Anastasios Kyrillidis , Siddhartha Satpathi

Recent research has shown that the properties of overcomplete Gabor frames and frames arising from shift-invariant systems form a precise match with certain conditions that are necessary for a frame in $L^2(\mathbf R)$ to have a…

Functional Analysis · Mathematics 2017-05-02 Ole Christensen , Marzieh Hasannasab

We study generative compressed sensing when the measurement matrix is randomly subsampled from a unitary matrix (with the DFT as an important special case). It was recently shown that $\textit{O}(kdn\| \boldsymbol{\alpha}\|_{\infty}^{2})$…

Information Theory · Computer Science 2023-11-21 Aaron Berk , Simone Brugiapaglia , Yaniv Plan , Matthew Scott , Xia Sheng , Ozgur Yilmaz