WORK ON MATHEMATICAL PROBLEMS RELATED TO A/D CONVERSION
BOOK CHAPTERS
Quantization, finite frames, and error diffusion, with A. Dunkel, A. Powell, and A. Spaeth, Proceedings of Symposia in Applied Mathematics on Finite Frame Theory: A Complete Introduction to Overcompleteness, AMS PSAPM Book Series Vol 73 (edited by Kasso Okoudjou) , pp. 143--174, 2016.
Noise-shaping Quantization Methods for Frame-based and Compressive Sampling Systems [arXiv:1502.05807], with E. Chou, S. Gunturk, F. Krahmer and R. Saab, Chapter 4 in "Sampling Theory, A Renaissance" (edited by G. Pfander), pp. 157—184, Birkhäuser, Boston, 2015.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
Learning tensors from partial binary measurements [arXiv:1804.00108],
with N. Ghadermarzy and Y.Plan. Submitted.
Memoryless scalar quantization for random frames [arXiv:1804.02839], with K. Melnykova. Submitted.
From compressed sensing to compressed bit-streams:
practical encoders, tractable decoders [arXiv:1604.00700]
[journal
version], with R. Saab and R. Wang. IEEE
Transactions on Information Theory. Available online.
Quantization of compressive samples with stable and
robust recovery [arXiv:1504.00087],
with R. Saab and R. Wang. Applied and
Computational Harmonic Analysis. 44(1):123–143
(2018)
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
Deterministic Compressed Sensing and Quantization [journal version],
with A. Ahmadieh. SPIE Wavelets and Sparsity XVI,
San Diego, Aug 2015.
Near-optimal compression for compressed sensing, with
R. Saab and R. Wang, Data Compression Conference 2015
(DCC2015), accepted.
Sigma-Delta quantization of sub-Gaussian compressed
sensing measurements [journal
version], with F. Krahmer and R. Saab. Proceedings
of International Conference on Sampling
Theory and Applications (SampTA) 2013.
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).