Adcock, Ben, Anders C. Hansen, and Bogdan Roman. 2015.
“The Quest for Optimal Sampling: Computationally Efficient, Structure-Exploiting Measurements for Compressed Sensing.” In
Compressed Sensing and Its Applications: MATHEON Workshop 2013, edited by Holger Boche, Robert Calderbank, Gitta Kutyniok, and Jan Vybíral, 143–67. Applied and
Numerical Harmonic Analysis.
Cham:
Springer International Publishing.
https://doi.org/10.1007/978-3-319-16042-9_5.
Baraniuk, Richard G., Volkan Cevher, Marco F. Duarte, and Chinmay Hegde. 2010.
“Model-Based Compressive Sensing.” IEEE Transactions on Information Theory 56 (4): 1982–2001.
https://doi.org/10.1109/TIT.2010.2040894.
Baraniuk, Richard, Mark Davenport, Ronald DeVore, and Michael Wakin. 2008.
“A Simple Proof of the Restricted Isometry Property for Random Matrices.” Constructive Approximation 28 (3): 253–63.
https://doi.org/10.1007/s00365-007-9003-x.
Barron, Andrew R., Albert Cohen, Wolfgang Dahmen, and Ronald A. DeVore. 2008.
“Approximation and Learning by Greedy Algorithms.” The Annals of Statistics 36 (1, 1): 64–94.
https://doi.org/10.1214/009053607000000631.
Cai, T. Tony, Guangwu Xu, and Jun Zhang. 2008.
“On Recovery of Sparse Signals via ℓ1 Minimization.” May 1, 2008.
http://arxiv.org/abs/0805.0149.
Candès, Emmanuel J. 1999.
“Harmonic Analysis of Neural Networks.” Applied and Computational Harmonic Analysis 6 (2): 197–218.
https://doi.org/10.1006/acha.1998.0248.
Candès, Emmanuel J., Yonina C. Eldar, Deanna Needell, and Paige Randall. 2011.
“Compressed Sensing with Coherent and Redundant Dictionaries.” Applied and Computational Harmonic Analysis 31 (1): 59–73.
https://doi.org/10.1016/j.acha.2010.10.002.
Candès, Emmanuel J., Justin K. Romberg, and Terence Tao. 2006.
“Stable Signal Recovery from Incomplete and Inaccurate Measurements.” Communications on Pure and Applied Mathematics 59 (8): 1207–23.
https://doi.org/10.1002/cpa.20124.
Candès, Emmanuel J., and Terence Tao. 2006.
“Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?” IEEE Transactions on Information Theory 52 (12): 5406–25.
https://doi.org/10.1109/TIT.2006.885507.
———. 2008. “The Uniform Uncertainty Principle and Compressed Sensing.”
Candès, Emmanuel, and Terence Tao. 2005.
“Decoding by Linear Programming.” IEEE Transactions on Information Theory 51 (12): 4203–15.
https://doi.org/10.1109/TIT.2005.858979.
Christensen, Ole. 2016.
An Introduction to Frames and Riesz Bases. Second edtion. Applied and
Numerical Harmonic Analysis.
Cham:
Springer International Publishing.
https://doi.org/10.1007/978-3-319-25613-9.
Daubechies, I. 1990.
“The Wavelet Transform, Time-Frequency Localization and Signal Analysis.” IEEE Transactions on Information Theory 36 (5): 961–1005.
https://doi.org/10.1109/18.57199.
Daubechies, Ingrid. 1992.
Ten Lectures on Wavelets.
Philadelphia, Pa:
Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104).
http://epubs.siam.org/doi/book/10.1137/1.9781611970104.
Daubechies, Ingrid, Ronald DeVore, Massimo Fornasier, and C. Si̇nan Güntürk. 2010.
“Iteratively Reweighted Least Squares Minimization for Sparse Recovery.” Communications on Pure and Applied Mathematics 63 (1): 1–38.
https://doi.org/10.1002/cpa.20303.
Donoho, D. L., M. Elad, and V. N. Temlyakov. 2006.
“Stable Recovery of Sparse Overcomplete Representations in the Presence of Noise.” IEEE Transactions on Information Theory 52 (1): 6–18.
https://doi.org/10.1109/TIT.2005.860430.
Donoho, David L. 2006.
“Compressed Sensing.” IEEE Transactions on Information Theory 52 (4): 1289–1306.
https://doi.org/10.1109/TIT.2006.871582.
Donoho, David L., and Michael Elad. 2003.
“Optimally Sparse Representation in General (nonorthogonal) Dictionaries via ℓ1 Minimization.” Proceedings of the National Academy of Sciences 100 (5): 2197–2202.
https://doi.org/10.1073/pnas.0437847100.
Duffin, R. J., and A. C. Schaeffer. 1952.
“A Class of Nonharmonic Fourier Series.” Transactions of the American Mathematical Society 72 (2): 341–66.
https://doi.org/10.2307/1990760.
Flammia, Steven T., David Gross, Yi-Kai Liu, and Jens Eisert. 2012.
“Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity, and Efficient Estimators.” New Journal of Physics 14 (9): 095022.
https://doi.org/10.1088/1367-2630/14/9/095022.
Foygel, Rina, and Nathan Srebro. 2011.
“Fast-Rate and Optimistic-Rate Error Bounds for L1-Regularized Regression.” August 1, 2011.
http://arxiv.org/abs/1108.0373.
Geer, Sara van de. 2014.
“Worst Possible Sub-Directions in High-Dimensional Models.” In. Vol. 131.
http://arxiv.org/abs/1403.7023.
Hegde, Chinmay, and Richard G. Baraniuk. 2012.
“Signal Recovery on Incoherent Manifolds.” IEEE Transactions on Information Theory 58 (12): 7204–14.
https://doi.org/10.1109/TIT.2012.2210860.
Heil, C., and D. Walnut. 1989.
“Continuous and Discrete Wavelet Transforms.” SIAM Review 31 (4): 628–66.
https://doi.org/10.1137/1031129.
Jung, Alexander, Nguyen Tran Quang, and Alexandru Mara. 2017.
“When Is Network Lasso Accurate?” April 7, 2017.
http://arxiv.org/abs/1704.02107.
Kovačević, Jelena, and Amina Chebira. 2008.
An Introduction to Frames. Vol. 2.
https://doi.org/10.1561/2000000006.
Krahmer, Felix, Gitta Kutyniok, and Jakob Lemvig. 2014.
“Sparse Matrices in Frame Theory.” Computational Statistics 29 (3-4): 547–68.
https://doi.org/10.1007/s00180-013-0446-1.
Lederer, Johannes, and Michael Vogt. 2020.
“Estimating the Lasso’s Effective Noise.” April 24, 2020.
http://arxiv.org/abs/2004.11554.
Meinshausen, Nicolai, and Peter Bühlmann. 2006.
“High-Dimensional Graphs and Variable Selection with the Lasso.” The Annals of Statistics 34 (3): 1436–62.
https://doi.org/10.1214/009053606000000281.
Meinshausen, Nicolai, and Bin Yu. 2009.
“Lasso-Type Recovery of Sparse Representations for High-Dimensional Data.” The Annals of Statistics 37 (1): 246–70.
https://doi.org/10.1214/07-AOS582.
Mixon, Dustin G. 2012.
“Sparse Signal Processing with Frame Theory.” http://arxiv.org/abs/1204.5958.
Morgenshtern, Veniamin I., and Helmut Bölcskei. 2011.
“A Short Course on Frame Theory.” http://arxiv.org/abs/1104.4300.
Needell, Deanna, and Roman Vershynin. 2009.
“Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit.” Foundations of Computational Mathematics 9 (3): 317–34.
https://doi.org/10.1007/s10208-008-9031-3.
Raskutti, Garvesh, Martin J. Wainwright, and Bin Yu. 2010.
“Restricted Eigenvalue Properties for Correlated Gaussian Designs.” 2 11: 2241–59.
http://www.jmlr.org/papers/volume11/raskutti10a/raskutti10a.pdf.
Ravikumar, Pradeep, Martin J. Wainwright, Garvesh Raskutti, and Bin Yu. 2011.
“High-Dimensional Covariance Estimation by Minimizing ℓ1-Penalized Log-Determinant Divergence.” Electronic Journal of Statistics 5: 935–80.
https://doi.org/10.1214/11-EJS631.
Rish, Irina, and Genady Grabarnik. 2014.
“Sparse Signal Recovery with Exponential-Family Noise.” In
Compressed Sensing & Sparse Filtering, edited by Avishy Y. Carmi, Lyudmila Mihaylova, and Simon J. Godsill, 77–93. Signals and
Communication Technology.
Springer Berlin Heidelberg.
https://doi.org/10.1007/978-3-642-38398-4_3.
Soni, Akshay, and Yashar Mehdad. 2017.
“RIPML: A Restricted Isometry Property Based Approach to Multilabel Learning.” February 16, 2017.
http://arxiv.org/abs/1702.05181.
Wu, R., W. Huang, and D. R. Chen. 2013.
“The Exact Support Recovery of Sparse Signals With Noise via Orthogonal Matching Pursuit.” IEEE Signal Processing Letters 20 (4): 403–6.
https://doi.org/10.1109/LSP.2012.2233734.
Young, Robert M. 2001.
An Introduction to Non-Harmonic Fourier Series, Revised Edition, 93.
Academic Press.
http://books.google.com?id=Y2CBBcDlo5kC.
Zhang, Cun-Hui. 2010.
“Nearly Unbiased Variable Selection Under Minimax Concave Penalty.” The Annals of Statistics 38 (2): 894–942.
https://doi.org/10.1214/09-AOS729.
Zhao, Peng, and Bin Yu. 2006.
“On Model Selection Consistency of Lasso.” Journal of Machine Learning Research 7: 2541–63.
http://www.jmlr.org/papers/volume7/zhao06a/zhao06a.
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