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WORK ON MATHEMATICAL PROBLEMS RELATED TO A/D CONVERSION

 

BOOK CHAPTER

Quantization and Finite Frames, Chapter 8 (pages 267-302) in "Finite frames: Theory and Applications" (edited by P. Casazza and G. Kutyniok), Birkhauser, Boston, 2012.

 

JOURNAL PAPERS

Sigma-Delta quantization of sub-Gaussian frame expansions and its application to compressed sensing [arXiv:1306.4549], with F. Krahmer and R. Saab. Submitted.

Sobolev duals for random frames and sigma-delta quantization of compressed sensing measurements [preprint version][journal version], with S. Güntürk, M. Lammers, A. Powell, and R. Saab. Foundations of Computational Mathematics. 13(1):1–36 (2013).

Coarse quantization for random interleaved sampling of bandlimited signals [preprint version][journal version], with A. Powell, J. Tanner, and Y. Wang, ESAIM: Mathematical Modelling and Numerical Analysis. 46(3):605- 618, 2012.

The Golden Ratio Encoder [arXiv:0809.1257v1] [journal version], with I. Daubechies, S. Güntürk, and Y. Wang, IEEE Transactions on Information Theory, 56(10):5097-5110, 2010.

Sobolev duals in frame theory and sigma-delta quantization [preprint version] [journal version] [erratum], with J. Blum, M. Lammers, and A. Powell, Journal of Fourier Analysis and Applications, 16(3):365-381, 2010.

Alternative dual frames for digital-to-analog conversion in sigma-delta quantization [preprint version] [journal version], with M. Lammers and A. Powell, Advances in Computational Mathematics, 32(1):73-102, 2010.

Robust and practical analog-to-digital conversion with exponential precision [preprint version] [journal version],  with I. Daubechies, IEEE Transactions on Information Theory, 52(8):3533-3545, 2006.

Sigma-Delta quantization and finite frames [preprint verision] [journal version], with J. Benedetto and A. Powell, IEEE Transactions on Information Theory, 52(5):1990-2005, 2006.

Second order Sigma-Delta quantization of finite frame expansions [preprint version] [journal version], with J. Benedetto and A. Powell, Applied and Computational Harmonic Analysis, 20(1):126-148, 2006.

On coarse quantization of tight Gabor frame expansions [preprint version] [journal version], International Journal of Wavelets, Multiresolution and Information Processing, 3(2):283-299, 2005.

Coarse quantization of highly redundant time-frequency representations of square-integrable functions [preprint version] [journal version], Applied and Computational Harmonic Analysis, 14(2):107-132, 2003.

Stability analysis for several sigma-delta methods of coarse quantization of bandlimited functions [preprint version] [journal version], Constructive Approximation, 18(4):599-623, 2002.  

 

CONFERENCE PROCEEDINGS

Sigma-Delta quantization for compressed sensing [journal version], Proceedings of Conference on Information Sciences and Systems (CISS) 2010, with S. Güntürk, M. Lammers, A. Powell, and R. Saab.

Sobolev duals of random frames [journal version], Proceedings of Conference on Information Sciences and Systems (CISS) 2010, with S. Güntürk, M. Lammers, A. Powell, and R. Saab.

On quantization of finite frame expansions: sigma-delta schemes of arbitrary order [preprint version] [journal version], with M. Lammers and A. Powell, SPIE, Wavelets XII, San Diego, Aug. 2007.

Analog-to-digital conversion for finite frames [preprint version] [journal version], SPIE, Wavelets XI, San Diego, Jul. 2005, (invited), with J. Benedetto and A. Powell,

Sigma-delta quantization and finite frames [preprint version] [journal version], with J. Benedetto and A. Powell, Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, May 2004, pp. 937 - 940, (invited).