Unlocking New Capabilities in the Analysis of GC × GC‐TOFMS Data With Shift‐Invariant Multi‐Linearity
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Chemometrics"
DOI: 10.1002/cem.3623
Abstract: This paper introduces a novel deconvolution algorithm, shift‐invariant multi‐linearity (SIML), which significantly enhances the analysis of data from two‐dimensional gas chromatography instruments coupled to a time‐of‐flight mass spectrometer (GC × GC‐TOFMS). Designed to address the challenges posed… read more here.
Keywords: shift invariant; shift; invariant multi; unlocking new ... See more keywords
An adaptive sampling method for high-dimensional shift-invariant signals
Sign Up to like & getrecommendations! Published in 2017 at "Mathematical Methods in The Applied Sciences"
DOI: 10.1002/mma.4323
Abstract: In this paper, an adaptive method for sampling and reconstructing high-dimensional shift-invariant signals is proposed. First, the integrate-and-fire sampling scheme and an approximate reconstruction algorithm for one-dimensional bandlimited signals are generalized to shift-invariant signals. Then,… read more here.
Keywords: shift; high dimensional; invariant signals; shift invariant ... See more keywords
Representing Kernels of Perturbations of Toeplitz Operators by Backward Shift-Invariant Subspaces
Sign Up to like & getrecommendations! Published in 2020 at "Integral Equations and Operator Theory"
DOI: 10.1007/s00020-020-02592-7
Abstract: It is well known that the kernel of a Toeplitz operator is nearly invariant under the backward shift $S^*$. This paper shows that kernels of finite-rank perturbations of Toeplitz operators are nearly $S^*$-invariant with finite… read more here.
Keywords: toeplitz operators; backward shift; perturbations toeplitz; representing kernels ... See more keywords
Sampling in quasi shift-invariant spaces and Gabor frames generated by ratios of exponential polynomials
Sign Up to like & getrecommendations! Published in 2024 at "Mathematische Annalen"
DOI: 10.1007/s00208-024-03011-7
Abstract: We introduce two families of generators (functions) G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {G}}$$\end{document} that consist of entire and meromorphic functions enjoying a certain periodicity property and contain the classical Gaussian… read more here.
Keywords: quasi shift; shift invariant; invariant spaces; shift ... See more keywords
Analogs of the Lebesgue Measure and Diffusion in a Hilbert Space
Sign Up to like & getrecommendations! Published in 2019 at "International Journal of Theoretical Physics"
DOI: 10.1007/s10773-019-04224-2
Abstract: We study shift-invariant measures on a real separable Hilbert space E , which are also invariant with respect to orthogonal transforms. In this article a finitely additive analogue of the Lebesgue measure is constructed. It… read more here.
Keywords: hilbert space; shift invariant; lebesgue measure; space ... See more keywords
Compressive sampling and reconstruction in shift-invariant spaces associated with the fractional Gabor transform
Sign Up to like & getrecommendations! Published in 2021 at "Defence Technology"
DOI: 10.1016/j.dt.2021.04.003
Abstract: Abstract In this paper, we propose a compressive sampling and reconstruction system based on the shift-invariant space associated with the fractional Gabor transform. With this system, we aim to achieve the sub-Nyquist sampling and accurate… read more here.
Keywords: reconstruction; system; sampling reconstruction; compressive sampling ... See more keywords
Nonuniform sampling in principal shift-invariant subspaces of mixed Lebesgue spaces Lp,q(Rd+1)
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.04.036
Abstract: Abstract In this paper, we study the nonuniform sampling and reconstruction problem in shift-invariant subspaces of mixed Lebesgue spaces. We first show that shift-invariant subspaces in mixed Lebesgue spaces L p , q ( R… read more here.
Keywords: subspaces mixed; mixed lebesgue; lebesgue spaces; shift invariant ... See more keywords
Selective learning for sensing using shift-invariant spectrally stable undersampled networks
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DOI: 10.1038/s41598-024-83706-8
Abstract: The amount of data collected for sensing tasks in scientific computing is based on the Shannon-Nyquist sampling theorem proposed in the 1940s. Sensor data generation will surpass 73 trillion GB by 2025 as we increase… read more here.
Keywords: shift invariant; invariant spectrally; selective learning; spectrally stable ... See more keywords
Dynamical sampling in multiply generated shift-invariant spaces
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DOI: 10.1080/00036811.2016.1157586
Abstract: In this paper, we study the problem of dynamical sampling in multiply generated shift-invariant spaces. We give a necessary and sufficient condition for stable reconstruction of signals in multiply generated shift-invariant spaces. Moreover, we show… read more here.
Keywords: shift; shift invariant; generated shift; multiply generated ... See more keywords
Semi-Average Sampling for Shift-Invariant Signals in a Mixed Lebesgue Space
Sign Up to like & getrecommendations! Published in 2020 at "Numerical Functional Analysis and Optimization"
DOI: 10.1080/01630563.2020.1737815
Abstract: Abstract This article mainly studies the nonuniform and semi-average sampling of time-varying shift-invariant signals living in a mixed Lebesgue space under the condition that the generator of the shift-invariant subspace belongs to a hybrid-norm space… read more here.
Keywords: invariant signals; space; shift invariant; semi average ... See more keywords
Reconstruction from convolution random sampling in local shift invariant spaces
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DOI: 10.1088/1361-6420/ab40f7
Abstract: In this paper, we consider the problem of reconstructing functions in local multiply generated shift invariant spaces from convolution random samples. The sampling set is randomly chosen with one kind of probability distribution over a… read more here.
Keywords: convolution random; shift invariant; invariant spaces;