On stability of sampling-reconstruction models

被引：15

作者：

Acosta-Reyes, Ernesto ^{[1
]}

Aldroubi, Akram ^{[1
]}

Krishtal, Ilya ^{[2
]}

机构：

[1] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

[2] No Illinois Univ, Dept Math Sci, De Kalb, IL 60115 USA

来源：

ADVANCES IN COMPUTATIONAL MATHEMATICS | 2009年 / 31卷 / 1-3期

基金：

美国国家科学基金会;

关键词：

Irregular sampling; Non-uniform sampling; Sampling; Reconstruction; Jitter; Measurement error; Model error; SHIFT-INVARIANT SPACES; LANDAU-TYPE THEOREMS; GABOR FRAMES; SUBSPACES;

D O I：

10.1007/s10444-008-9083-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this paper we prove this result for a large class of sampling models. We define different classes of perturbations and present a way of quantifying the robustness of a model with respect to them. We also use the theory of localized frames to study the dual frame method for recovering the original signal from its samples.

引用

页码：5 / 34

页数：30

共 25 条

[1] Robustness of sampling and reconstruction and Beurling-Landau-type theorems for shift-invariant spaces [J].

Aldroubi, A ;

Krishtal, I .

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2006, 20 (02) :250-260

[2] Non-uniform weighted average sampling and reconstruction in shift-invariant and wavelet spaces [J].

Aldroubi, A .

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 2002, 13 (02) :151-161

[3] Beurling-Landau-type theorems for non-uniform sampling in shift invariant spline spaces [J].

Aldroubi, A ;

Gröchenig, K .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2000, 6 (01) :93-103

[4] Nonuniform sampling and reconstruction in shift-invariant spaces [J].

Aldroubi, A ;

Gröchenig, K .

SIAM REVIEW, 2001, 43 (04) :585-620

[5]

ALDROUBI A, 2007, ARXIV07054304

[6]

ALDROUBI A, 2008, SAMPL THEOR IN PRESS

[7]

Atreas N., 2002, SAMPL THEORY SIGNAL, V1, P261

[8] Asymptotic estimates for the entries of the matrices of inverse operators and harmonic analysis [J].

Baskakov, AG .

SIBERIAN MATHEMATICAL JOURNAL, 1997, 38 (01) :10-22

[9]

Benedetto J.J., 2001, APPL NUMER HARMON AN

[10]

Benedetto J.J., 2001, NONUNIFORM SAMPLING, P585

← 1 2 3 →