Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/reconstructing-signals-with-finite-rate-of-innovation-from-noisy-zCcZszBLXn
References (45)
-
V. Rabinovich, S. Roch (2006)
Reconstruction of Input Signals in Time-Varying FiltersNumerical Functional Analysis and Optimization, 27
-
A. Jerri (1979)
Correction to "The Shannon sampling theorem—Its various extensions and applications: A tutorial review", 67
-
Qiyu Sun (2008)
Frames in spaces with finite rate of innovationAdvances in Computational Mathematics, 28
-
K. Gröchenig, H. Schwab (2002)
Fast Local Reconstruction Methods for Nonuniform Sampling in Shift-Invariant SpacesSIAM J. Matrix Anal. Appl., 24
-
M. Nashed, G. Wahba (1974)
Generalized Inverses in Reproducing Kernel Spaces: An Approach to Regularization of Linear Operator EquationsSiam Journal on Mathematical Analysis, 5
-
S. Ramani, D. Ville, T. Blu, M. Unser (2008)
Nonideal Sampling and Regularization TheoryIEEE Transactions on Signal Processing, 56
-
R. Schaback, H. Wendland (2006)
Kernel techniques: From machine learning to meshless methodsActa Numerica, 15
-
Qiyu Sun (2006)
WIENER’S LEMMA FOR INFINITE MATRICES -
Yonina Eldar, M. Unser (2006)
Nonideal sampling and interpolation from noisy observations in shift-invariant spacesIEEE Transactions on Signal Processing, 54
-
Extrapolation and Interpolation) -
Johannes Sj (1994)
AN ALGEBRA OF PSEUDODIFFERENTIAL OPERATORS -
A. Tarczynski (1997)
Sensitivity of signal reconstructionIEEE Signal Processing Letters, 4
-
S. Smale, Ding-Xuan Zhou (2005)
Shannon sampling II: Connections to learning theoryApplied and Computational Harmonic Analysis, 19
-
A. Aldroubi, K. Gröchenig (2001)
Nonuniform Sampling and Reconstruction in Shift-Invariant SpacesSIAM Rev., 43
-
L. Schumaker (1981)
Spline Functions: Basic Theory -
Bi is with the Department of Scientific Computing and Computer Applications -
H. Feichtinger, K. Grōchenig, T. Strohmer (1995)
Efficient numerical methods in non-uniform sampling theoryNumerische Mathematik, 69
-
Stéphane Jaffard (1990)
Propriétés des matrices « bien localisées » près de leur diagonale et quelques applicationsAnnales De L Institut Henri Poincare-analyse Non Lineaire, 7
-
H.G. Feichtinger, K. Gröchenig, T. Strohmer (1995)
Efficient numerical methods in non-uniform sampling theoryNumer. Math., 69
-
A. Aldroubi, Qiyu Sun, Wai-Shing Tang (2005)
Convolution, Average Sampling, and a Calderon Resolution of the Identity for Shift-Invariant SpacesJournal of Fourier Analysis and Applications, 11
-
I. Maravic, M. Vetterli (2005)
Sampling and reconstruction of signals with finite rate of innovation in the presence of noiseIEEE Transactions on Signal Processing, 53
-
E-mail address: qsun@mail.ucf.edu -
M. Unser (2000)
Sampling-50 years after ShannonProceedings of the IEEE, 88
-
Y. Hao, P. Marziliano, M. Vetterli, T. Blu (2005)
Compression of ECG as a Signal with Finite Rate of Innovation2005 IEEE Engineering in Medicine and Biology 27th Annual Conference
-
G. Wahba (1990)
Spline Models for Observational Data -
P. Marziliano, M. Vetterli, T. Blu (2006)
Sampling and exact reconstruction of bandlimited signals with shot noiseIEEE Trans. Inform. Theory, 52
-
Nashed is with the Department of Mathematics -
Pancham Shukla, P. Dragotti (2007)
Sampling Schemes for Multidimensional Signals With Finite Rate of InnovationIEEE Transactions on Signal Processing, 55
-
H. Oraizi (2006)
Application of the method of least squares to electromagnetic engineering problemsIEEE Antennas Propag. Mag., 48
-
H. Oraizi (2006)
Application of the method of least to electromagnetic engineering problemsIEEE Antennas and Propagation Magazine, 48
-
Qiyu Sun (2006)
Nonuniform Average Sampling and Reconstruction of Signals with Finite Rate of InnovationSIAM J. Math. Anal., 38
-
G. Golub, C. Loan (1996)
Matrix computations (3rd ed.) -
Yonina Eldar, T. Dvorkind (2006)
A minimum squared-error framework for generalized samplingIEEE Transactions on Signal Processing, 54
-
P.L. Dragotti, M. Vetterli, T. Blu (2007)
Sampling moments and reconstructing signals of finite rate of innovation: Shannon meets Strans-FixIEEE Trans. Signal Process., 55
-
P. Marziliano, M. Vetterli, T. Blu (2006)
Sampling and exact reconstruction of bandlimited signals with additive shot noiseIEEE Transactions on Information Theory, 52
-
R. Marks (1990)
Introduction to Shannon Sampling and Interpolation Theory -
T. Blu, P. Dragotti, M. Vetterli, P. Marziliano, Lionel Coulot (2008)
Sparse Sampling of Signal InnovationsIEEE Signal Processing Magazine, 25
-
M. Unser, A. Aldroubi (1994)
A general sampling theory for nonideal acquisition devicesIEEE Trans. Signal Process., 42
-
S. Smale, Ding-Xuan Zhou (2004)
Shannon sampling and function reconstruction from point valuesBulletin of the American Mathematical Society, 41
-
J. Kusuma, I. Maravic, M. Vetterli (2003)
Sampling with finite rate of innovation: channel and timing estimation for UWB and GPSIEEE International Conference on Communications, 2003. ICC '03., 5
-
T. Blu, P. Dragotti, M. Vetterli, P. Marziliano, Lionel Coulot (2007)
Sparse Sampling of Signal Innovations: Theory, Algorithms and Performance Bounds -
R. Cramer, R. Scholtz, M. Win (2002)
Evaluation of an ultra-wide-band propagation channelIEEE Transactions on Antennas and Propagation, 50
-
M. Vetterli, P. Marziliano, T. Blu (2002)
Sampling signals with finite rate of innovationIEEE Trans. Signal Process., 50
-
A. Jerri (1977)
The Shannon sampling theorem—Its various extensions and applications: A tutorial reviewProceedings of the IEEE, 65
-
Andrzej Chrzeszczyk, Jan Kochanowski (2011)
Matrix Computations
- Publisher
- Springer Journals
- Copyright
- Copyright © 2009 by Springer Science+Business Media B.V.
- Subject
- Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/s10440-009-9474-9
- Publisher site
- See Article on Publisher Site
Abstract
A signal is said to have finite rate of innovation if it has a finite number of degrees of freedom per unit of time. Reconstructing signals with finite rate of innovation from their exact average samples has been studied in Sun (SIAM J. Math. Anal. 38, 1389–1422, 2006). In this paper, we consider the problem of reconstructing signals with finite rate of innovation from their average samples in the presence of deterministic and random noise. We develop an adaptive Tikhonov regularization approach to this reconstruction problem. Our simulation results demonstrate that our adaptive approach is robust against noise, is almost consistent in various sampling processes, and is also locally implementable.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Feb 24, 2009