Approximation of functions with one-bit neural networks
(with Weilin Li)
arXiv: 2112.09181
Approximation with one-bit polynomials in Bernstein form
(with Weilin Li)
arXiv: 2112.09183
Quantization for Spectral Super-resolution
(with Weilin Li)
Constructive Approximation, 2022.
arXiv: 2103.00079
Unrestricted (random) products of projections in Hilbert space:
Regularity, absolute convergence of trajectories, and statistics of
displacements
(with N.T. Thao) [pdf]
to appear in Pure and Applied Functional Analysis, 2022.
Convergence of the randomized Kaczmarz method for phase retrieval (with H. Jeong)
arXiv: 1706.10291
Distributed Noise-Shaping Quantization: II. Classical Frames (with E. Chou) [pdf]
in Excursions in Harmonic Analysis, Volume 5, pp 179--198, 2017.
Distributed Noise-Shaping Quantization: I. Beta Duals of Finite Frames and Near-Optimal Quantization of Random Measurements (with E. Chou)
Constructive Approximation, Vol. 44, Issue 1, pp 1–22, 2016.
arXiv: 1405.4628
Sobolev Duals for Random
Frames and Sigma-Delta Quantization of Compressed Sensing
Measurements (with M. Lammers, A. Powell, R. Saab,
and Ö. Yılmaz)
Foundations of Computational
Mathematics Vol. 13, No. 1, pp.1-36, 2013. [pdf]
On the Periodized Square of
L² 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]
Simultaneous and Hybrid beta-Encodings
CISS, 2008. doi.org/10.1109/CISS.2008.4558620 [pdf]
Approximation by Power
Series with ±1 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.