Publications of Sinan Gunturk

Publications of C. Sinan Güntürk

Journal and book articles

Mathematics of Analog-to-Digital Conversion
Communications on Pure and Applied Mathematics, Vol. 65, No. 12, 2012, pp.1671-1696 (Special Issue Commemorating the 75th Anniversary of the Courant Institute).
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]
Iteratively Re-weighted Least Squares Minimization for Sparse Recovery (with I. Daubechies, R. DeVore, and M. Fornasier)
Communications on Pure and Applied Mathematics, Vol. 63, no. 1, 2010, pp.1-38. arxiv:0807.0575
The Golden Ratio Encoder (with I. Daubechies, Y. Wang and O. Yilmaz)
IEEE Transactions on Information Theory, (56) (10):5097-5110, October 2010. [pdf]
A/D Conversion with Imperfect Quantizers (with I. Daubechies, R. DeVore and V. Vaishampayan)
IEEE Transactions on Information Theory, 52 (3):874-885, March 2006. [pdf]
Approximation by Power Series with $\pm 1$ 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.

Thesis

Harmonic Analysis of Two Problems in Signal Quantization and Compression, Princeton University, 2000. [pdf]

In Proceedings

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.