Sampling in the shift-invariant space generated by the bivariate Gaussian function

被引:1
|
作者
Romero, Jose Luis [1 ,2 ]
Ulanovskii, Alexander [3 ]
Zlotnikov, Ilya [1 ]
机构
[1] Univ Vienna, Fac Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria
[2] Austrian Acad Sci, Acoust Res Inst, Dr Ignaz Seipel-Pl 2, A-1010 Vienna, Austria
[3] Univ Stavanger, Dept Math & Phys, N-4036 Stavanger, Norway
基金
奥地利科学基金会;
关键词
Sampling; Shift-invariant space; Bivariate Gaussian; Gabor frame; GABOR FRAMES; DENSITY; INTERPOLATION; THEOREMS;
D O I
10.1016/j.jfa.2024.110600
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study the space spanned by the integer shifts of a bivariate Gaussian function and the problem of reconstructing any function in that space from samples scattered across the plane. We identify a large class of lattices, or more generally semi- regular sampling patterns spread along parallel lines, that lead to stable reconstruction while having densities close to the critical value given by Landau's limit. At the critical density, we construct examples of sampling patterns for which reconstruction fails. In the same vein, we also investigate continuous sampling along non-uniformly scattered families of parallel lines and identify the threshold density of line configurations at which reconstruction is possible. In a remarkable contrast with Paley-Wiener spaces, the results are completely different for lines with rational or irrational slopes. Finally, we apply the sampling results to Gabor systems with bivariate Gaussian windows. As a main contribution, we provide a large list of new examples of Gabor frames with non-complex lattices having volume close to 1. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).
引用
收藏
页数:29
相关论文
共 50 条
  • [11] Invariance of a Shift-Invariant Space
    Akram Aldroubi
    Carlos Cabrelli
    Christopher Heil
    Keri Kornelson
    Ursula Molter
    Journal of Fourier Analysis and Applications, 2010, 16 : 60 - 75
  • [12] Sampling for shift-invariant and wavelet subspaces
    Hogan, JA
    Lakey, J
    WAVELET APPLICATIONS IN SIGNAL AND IMAGE PROCESSING VIII PTS 1 AND 2, 2000, 4119 : 36 - 47
  • [13] Dynamical Sampling in Shift-Invariant Spaces
    Aceska, Roza
    Aldroubi, Akram
    Davis, Jacqueline
    Petrosyan, Armenak
    COMMUTATIVE AND NONCOMMUTATIVE HARMONIC ANALYSIS AND APPLICATIONS, 2013, 603 : 139 - 148
  • [14] A sampling theorem for shift-invariant subspace
    Chen, W
    Itoh, S
    IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1998, 46 (10) : 2822 - 2824
  • [15] Nonuniform sampling in multiply generated shift-invariant subspaces of mixed lebesgue spaces
    Xing, Nan
    IAENG International Journal of Applied Mathematics, 2020, 50 (03) : 584 - 588
  • [16] Convolution random sampling in multiply generated shift-invariant spaces of Lp(Rd)
    Jiang, Yingchun
    Li, Wan
    ANNALS OF FUNCTIONAL ANALYSIS, 2020, 12 (01)
  • [17] Sampling set conditions in weighted multiply generated shift-invariant spaces and their applications
    Xian, Jun
    Li, Song
    APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2007, 23 (02) : 171 - 180
  • [18] Sampling and Average Sampling in Quasi Shift-Invariant Spaces
    Kumar, Anuj
    Sampath, Sivananthan
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2020, 41 (10) : 1246 - 1271
  • [19] On Stability of Finitely Generated Shift-Invariant Systems
    Morten Nielsen
    Journal of Fourier Analysis and Applications, 2010, 16 : 901 - 920
  • [20] Multivariate Dynamical Sampling in and Shift-Invariant Spaces
    Zhang, Qingyue
    Li, Zunxian
    NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2019, 40 (06) : 670 - 684