Distributed noise-shaping quantization: I. Beta duals of finite frames and near-optimal quantization of random measurements (with E. Chou)
arXiv: 1405.4628
Sobolev Duals for Random
Frames and Sigma-Delta Quantization of Compressed Sensing
Measurements (with M. Lammers, A. Powell, R. Saab,
and O. Yilmaz)
Foundations of Computational
Mathematics Vol. 13, No. 1, pp.1-36, 2013. [pdf]
On the Periodized Square of
L^{2} Cardinal Splines (with E. Giné and W.R.
Madych)
Experimental
Mathematics, Vol. 20, No. 2, 2011, pp.177-188.
An Optimal Family of
Exponentially Accurate One-Bit Sigma-Delta Quantization
Schemes (with P. Deift and F. Krahmer)
Communications
on Pure and Applied Mathematics, Vol. 64, No.
7, 2011, pp.883-919. [pdf]
Approximation by Power
Series with Coefficients
International Mathematics
Research Notices, 26 (2005), 1601-1610.
arXiv: math.CA/0503373
A New Upper Bound for Finite
Additive Bases (with Mel Nathanson)
Acta Arithmetica, vol.
124 (2006), 235-255. [pdf]
Ergodic Dynamics in
Sigma-Delta Quantization: Tiling Invariant Sets and Spectral
Analysis of Error (with N.T. Thao)
Advances
in
Applied Mathematics, 34 (2005), 523-560. [pdf]
One-Bit Sigma-Delta
Quantization with Exponential Accuracy
Communications
on
Pure and Applied Mathematics, vol. 56, pp. 1608-1630,
no. 11, 2003.
Approximating a Bandlimited
Function Using Very Coarsely Quantized Data: Improved Error
Estimates in Sigma-Delta Modulation
Journal
of
the American Mathematical Society, 17 (2004), 229-242.
Refined Error Analysis in
Second-Order Sigma Delta Modulation with Constant Inputs
(with N.T. Thao)
IEEE Transactions on Information Theory, 50
(5):839-860, May 2004. [pdf]
Number Theoretical Error
Estimates in a Quantization Scheme for Bandlimited Signals
Unusual
Applications
of Number Theory, DIMACS: Series in Discrete
Mathematics and Theoretical Computer Science, pp. 81-94,
Vol. 64, 2004, AMS Publications. [pdf]
On the Robustness of Single
Loop Sigma-Delta Modulation (with J.C. Lagarias and
V.A. Vaishampayan)
IEEE Transactions on Information Theory, 47
(5):1735-1744, July 2001. [pdf]
Permutation Based Design of
Filter Banks and Orthogonal Block Transforms (with H.
Caglar, E. Anarim and B. Sankur)
Multidimensional Systems and Signal Processing, 12
(1):63-79, January 2001.
VQ-Adaptive Block Transform
Coding of Images (with H. Caglar, E. Anarim and B.
Sankur)
IEEE Transactions on Image Processing, 7 (1):110-115,
January 1998.
Beta Expansions: A New
Approach to Digitally Correct A/D Conversion (with I.
Daubechies, R. DeVore and V. Vaishampayan)
Proc. IEEE International Symposium on Circuits and Systems
ISCAS'2002, Scottsdale, Arizona (May 2002), pp. 26-29.
Improved Error Estimates for
First Order Sigma-Delta Systems
Proc. International Workshop on Sampling Theory and
Applications (SampTA'99), Loen, Norway, 1999. [ps]
Matched Block Transform
Design Techniques (with H. Caglar, E. Anarim and B.
Sankur)
Proc. European Conference on Signal Processing
(EUSIPCO'96), Trieste, Italy, 1996.
A New Permutation Based
Orthogonal Block and Lapped Transform Design Technique
(with H. Caglar, E. Anarim and B. Sankur)
Proc. IEEE European Conference on Circuit Theory and Design
(ECCTD'95), Istanbul, Turkey, 1995.