College of Arts and Science Vanderbilt University
Vanderbilt Univeristy College of Arts and Science
Department of

Mathematics

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Publications

Papers

Error bounds for consistent reconstruction: random polytopes and coverage processes, (joint with J.T. Whitehouse), submitted.

Sobolev duals for random frames and Sigma-Delta quantization of compressed sensing measurements, (joint with C.S. Gunturk, M. Lammers, R. Saab, O. Yilmaz), Foundations of Computational Mathematics, 13 (2013), no. 1, 1-36.

Almost sure convergence for the Kaczmarz algorithm with random measurements, (joint with X. Chen), Journal of Fourier Analysis and Applications, 18 (2012), no. 6, 1195-1214.

Perturbations of measurement matrices and dictionaries in compressed sensing, (joint with A. Aldroubi and X. Chen), Applied and Computational Harmonic Analysis, 33 (2012), no. 2, 282-291.

A note on finite dual frame pairs, (joint with O. Christensen, X.C. Xiao), Proceedings of the AMS, 140 (2012), no. 11, 3921-3930.

Quantization and finite frames, (joint with R. Saab and O. Yilmaz), Chapter 8 (pages 267-302) in "Finite frames" (edited by P. Casazza and G. Kutyniok),  Birkhauser, Boston, 2012.

Coarse quantization for random interleaved sampling of bandlimited signals, (joint with J. Tanner, Y. Wang, O. Yilmaz), ESAIM Mathematical Modelling and Numerical Analysis, 46 (2012), 605-618.

Time-frequency concentration of generating systems, (joint with P. Jaming), Proceedings of the AMS, 139, (2011), 3279-3290.

Mean squared error bounds for the Rangan-Goyal soft thresholding algorithm, Applied and Computational Harmonic Analysis, 29, (2010), 251-271.

Sobolev duals in frame theory and sigma-delta quantization, (joint with J. Blum, M. Lammers and O. Yilmaz), Journal of Fourier Analysis and Applications, 16, (2010), 365-381.

Alternative dual frames for digital-to-analog conversion in Sigma-Delta quantization, (joint with M. Lammers and O. Yilmaz), Advances in Computational Mathematics, 32, (2010), 73-102.

Regularity for complete and minimal Gabor systems on a lattice, (joint with C. Heil), Illinois Journal of Mathematics, 53, (2009), 1077-1094.

Uncertainty principles for orthonormal sequences, (joint with P. Jaming), Journal of Functional Analysis, 243, (2007), 611-630.

Gabor Schauder bases and the Balian-Low Theorem, (joint with C. Heil), Journal of Mathematical Physics, 47, 113506 (2007), 21 pages.

An optimal example for the Balian-Low uncertainty principle, (joint with J. Benedetto and W. Czaja), SIAM Journal on Mathematical Analysis, 38, (2006), 333-345.

Recent developments in the Balian-Low Theorem, (joint with W. Czaja), in Harmonic Analysis and Applications (edited by C. Heil), Birkhauser, Boston, 2006.

Sigma-Delta quantization and finite frames, (joint with J. Benedetto and O. Yilmaz), IEEE Transactions on Information Theory, 52 (2006), 1990--2005.

An endpoint (1,infinity) Balian-Low Theorem, (joint with J. Benedetto, W. Czaja, J. Sterbenz), Mathematical Research Letters, 13 (2006), 467-474.

A (p,q) version of Bourgain's theorem, (joint with J. Benedetto), Transactions of the AMS, 358 (2006), 2489--2505.

Second order Sigma-Delta quantization of finite frame expansions, (joint with J. Benedetto and O. Yilmaz), Applied and Computational Harmonic Analysis, 20 (2006), 126--148.

Time-frequency mean and variance sequences of orthonormal bases, Journal of Fourier Analysis and Applications, 11 (2005), 375--387.

Orthonormalized coherent states, in Wavelets, Frames, and Operator Theory (C. Heil, P. Jorgenson, D. Larson, editors), AMS Contemporary Mathematics, 345 (2004), 283--297.

The Balian-Low Theorem and regularity of Gabor systems, (joint with J. Benedetto, W. Czaja, and P. Gadzinski), Journal of Geometric Analysis, 13 (2003), 239--254.

Conference Proceedings

Sigma Delta quantization for compressed sensing, 44th Annual Conference on Information Sciences and Systems (Princeton, NJ, March 2010), joint with C.S. Gunturk, M. Lammers, R. Saab, O. Yilmaz. 

Sobolev duals of random frames, 44th Annual Conference on Information Sciences and Systems (Princeton, NJ, March 2010), joint with C.S. Gunturk, M. Lammers, R. Saab, O. Yilmaz. 

Estimation algorithms with noisy frame coefficients, invited, Wavelets XII (San Diego, CA, 2007), SPIE Proc., SPIE Bellingham, WA, 2007.

On quantization of finite frame expansions: sigma-delta schemes of arbitrary order, invited, (joint with M. Lammers and O. Yilmaz), Wavelets XII (San Diego, CA, 2007), SPIE Proc., SPIE Bellingham, WA, 2007.

Analog to digital conversion for finite frames, invited, (joint with J. Benedetto and O. Yilmaz), Wavelets XI (San Diego, CA, 2005), SPIE Proc., SPIE Bellingham, WA, 2005.

Sigma-Delta quantization and finite frames, invited, (joint with J. Benedetto and O. Yilmaz), Proceedings of ICASSP-2004, IEEE International Conference on Acoustics, Speech, and Signal Processing, Montreal, May 2004.

MRI signal reconstruction by Fourier frames on interleaving spirals, (joint with J. Benedetto and H.-C. Wu), Proceedings of the 2002 IEEE International Symposium on Biomedical Imaging, Washington, DC, July 2002.