Compressed Sensing and Redundant Dictionaries

Holger Rauhut, Karin Schnass, Pierre Vandergheynst · IEEE Transactions on Information Theory · 2007

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Type: article
Published: 2007-01-04
Cited by: 580
References: 26
Access: Open access
DOI: https://doi.org/10.1109/tit.2008.920190
arXiv: https://arxiv.org/abs/math/0701131
OpenAlex: https://openalex.org/W2105877514
Semantic Scholar: https://api.semanticscholar.org/CorpusID:15742462

Keywords

Compressed sensing, Orthonormal basis, Restricted isometry property, Basis pursuit, Basis (linear algebra)

References

The Johnson-Lindenstrauss Lemma Meets Compressed SensingRichard G. Baraniuk, Mark A. Davenport, Ronald DeVore — 2006
Uniform Uncertainty Principle for Bernoulli and Subgaussian EnsemblesShahar Mendelson, Alain Pajor, Nicole Tomczak-Jaegermann — 2006
Atomic Decomposition by Basis PursuitScott Shaobing Chen, David L. Donoho, Michael A. Saunders — 1998
Probability Inequalities for the Sum of Independent Random VariablesG. G. Bennett — 1962
Weak Convergence and Empirical Processes: With Applications to StatisticsAad van der Vaart, Jon A. Wellner — 1996
Adaptive greedy approximationsGeoffrey M. Davis, Stéphane Mallat, M. Avellaneda — 1997
Sparse Approximate Solutions to Linear SystemsB. K. Natarajan — 1995
A Simple Proof of the Restricted Isometry Property for Random MatricesRichard G. Baraniuk, Mark A. Davenport, Ronald DeVore — 2008
For most large underdetermined systems of linear equations the minimal 𝓁1‐norm solution is also the sparsest solutionDavid L. Donoho — 2006
Database-friendly random projectionsDimitris Achlioptas — 2001
Random Sampling of Sparse Trigonometric PolynomialsHolger Rauhut — 2005
Fast Minimization by Iterative Thresholding for Multidimensional NMR SpectroscopyIddo Drori — 2007
Stable recovery of sparse overcomplete representations in the presence of noiseDavid L. Donoho, Michael Elad, Vladimir Temlyakov — 2006
Sparse reconstruction by convex relaxation: Fourier and Gaussian measurementsMark Rudelson, Roman Vershynin — 2006
Counting faces of randomly-projected polytopes when the projection radically lowers dimensionDavid L. Donoho, Jared Tanner — 2006
Greed is good: algorithmic results for sparse approximationJoel A. Tropp — 2004
Signal Recovery From Random Measurements Via Orthogonal Matching PursuitJoel A. Tropp, Anna C. Gilbert — 2007
Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?Emmanuel J. Candès, Terence Tao — 2004
Matching pursuits with time-frequency dictionariesStéphane Mallat, Zhifeng Zhang — 1993
Average Case Analysis of Multichannel ThresholdingRémi Gribonval, Boris Mailhé, Holger Rauhut — 2007

Cited by

Near Oracle Performance of Signal Space Greedy MethodsRaja Giryes, Deanna Needell — 2014
Compressive Parameter Estimation with EmdDian Mo — 2014
Optimal non-linear modelsAkram Aldroubi, Carlos Cabrelli, Ursula Molter — 2009
Compressed sensing using hidden Markov models with application to vision based aircraft trackingJason Ford, Timothy L. Molloy, Joanne L. Hall — 2014
Antipodal random sequences with prescribed second-order statistics: application to Compressive Sensing and UWB system based on DS-CDMAMauro Mangia — 2013
Compressed SensingYonina C. Eldar, Gitta Kutyniok — 2012
On Parameter Estimation Employing Sinewave Fit andPhase Noise Compensation in OFDM SystemsSenay Negusse — 2015
Applications of compressed sensing in computational physicsAndreas Solbrå — 2014
Sparsity promoting optimization in quantum mechanical signal processingRyan Compton — 2012
Spectrum Sensing using Compressed Sensing Techniques for Sparse Multiband SignalsK. P. Soman, P Avinash, R Gandhiraj — 2012
Use of tight frames for optimized compressed sensingKatsaggelos, A., Lisimachos P. Kondi, Evaggelia Tsiligianni — 2012
Compressed Sensing for Moving Imagery in Medical ImagingÇağdaş Bilen, Yao Wang, Ivan Selesnick — 2012
On the Null Space Property of -Minimization for in Compressed SensingYi Gao, Jigen Peng, Shigang Yue — 2015
Results on ECG compressed sensing using specific dictionaries and its validationMonica Fira, Liviu Goraş, Nicolae Cleju — 2012
Fast hard thresholding with Nesterov"s gradient methodVolkan Cevher, Sina Jafarpour — 2010
Single Image Super ResolutionP. B. Shreyas, Baxi Aatha — 2012
Rigorous optimization recipes for sparse and low rank inverse problems with applications in data sciencesAnastasios Kyrillidis — 2014
An Adaptive ISAR-Imaging-Considered Task Scheduling Algorithm for Multi-Function Phased Array RadarsYijun Chen, Qun Zhang, Ning Yuan — 2015
A survey on compressive sensingLi Shutao, Wei Dan — 2015
Compressive parameter estimation via K-median clusteringDian Mo, Marco F. Duarte — 2014

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