1. Improved Bounds on Restricted Isometry Constants for Gaussian Matrices; SIAM J. on Matrix Analysis, Vol. 31(5) (2010) 2882-2898. (with Bubacarr Bah)
2. Coarse quantization for random interleaved sampling of bandlimited signals; Mathematical Modelling and Numerical Analysis, Vol. 46(3) (2012) 605-618. (with Alexander M. Powell, Yang Wang, and Ozgur Yilmaz)
3. Phase transitions for greedy sparse approximation algorithms; Applied and Computational Harmonic Analysis, Vol. 30(2) (2011) 188-203. (with Jeffrey D. Blanchard, Coralia Cartis and Andrew Thompson)
4. Precise Undersampling Theorems; Proceedings of the IEEE, Vol. 98(6) (2010) 913-924. (with David L. Donoho)
5. Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing; Philosophical Transactions of The Royal Society A, Vol. 367(1906) (2009) 4273-4293. (with David L. Donoho)
Section 5 of this preprint is an online supplement of the published journal article.
6. Decay properties for restricted isometry constants; IEEE Signal Processing Letters, Vol. 16(7) (2009) 572-575.(with Jeffrey D. Blanchard and Coralia Cartis)
7. Compressed Sensing: How sharp is the Restricted Isometry Property?; SIAM Review, Vol. 53(1) (2011) 105-125. (with Jeffrey D. Blanchard and Coralia Cartis)
8. Counting the faces of randomly-projected hypercubes and orthants, with applications; Discrete and Computational Geometry, Vol. 43(3) (2010) 522-541. (with David L. Donoho)
9. Exponential bounds implying construction of compressed sensing matrices, error-correcting codes and neighborly polytopes by random sampling; IEEE Trans. on Information Theory, Vol. 56(4) (2010) 2002-2016. (with David L. Donoho)
10. Identification of Matrices having a Sparse Representation; IEEE Transactions on Signal Processing , Vol. 56(11) (2008) 5376-5388. (with Gotz E. Pfander and Holger Rauhut)
11. Counting faces of randomly-projected polytopes when the projection radically lowers dimension; Journal of the AMS , Vol. 22(1) (2009) 1-53. (with David L. Donoho)
12.
Neighborliness of
Randomly-Projected Simplices in High Dimensions; Proceedings of the
13.
Sparse Nonnegative
Solutions of Underdetermined Linear Equations by Linear Programming; Proceedings
of the
14. Robust reprojection methods for the resolution of Gibbs phenomenon ; Applied and Computational Harmonic Analysis, Vol. 20(1) (2006) 3-25. (with Anne Gelb)
15. Fast reconstruction methods for bandlimited functions from periodic nonuniform sampling ; SIAM J. on Numerical Analysis, Vol. 44(3) (2006) 1073-1094. (with Thomas Strohmer)
16. Optimal Filter and Mollifier for Piecewise Smooth Spectral Data ; Mathematics of Computation, Vol. 75(254) (2006) 767-790.
17. Adaptive Filters for Piecewise Smooth Spectral Data ; IMA Journal of Numerical Analysis, Vol. 25(4) (2005) 635-647. (with Eitan Tadmor)
18. Implementations of Shannon's sampling theorem, a time-frequency approach ; Sampling Theory in Signal and Image Processing, Vol. 4(1) (2005) 1-17. (with Thomas Strohmer)
19. Adaptive Mollifiers - High Resolution Recover of Piecewise Smooth Data from its Spectral Information ; Foundations of Computational Mathematics 2(2) (2002) 155-189. (with Eitan Tadmor)
1. Phase transitions for restricted isometry properties ; Proceedings of Signal Processing with Adaptive Sparse Structured Representations, April 2009. (with Jeffrey D. Blanchard and Coralia Cartis)
2. Fast reconstruction algorithms for periodic nonuniform sampling with applications to time-interleaved ADCs ; Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing, April 2007. (with Thomas Strohmer)
3. Thresholds for the Recovery of Sparse Solutions via L1 Minimization ; Proceedings of the Conference on Information Sciences and Systems, March 2006. (with David L. Donoho)
4.
An Adaptive Order Godunov Type
Central Scheme ; "Hyperbolic Problems: Theory, Numerics,
Applications", Proceedings of the 9th International Conference in