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- Ingrid Daubechies, Ronald A. DeVore, Massimo Fornasier, C. Sinan Güntürk
- 2008 42nd Annual Conference on Information…
- 2008

Given an mtimesN matrix Phi, with m<N, the system of equations Phix=y is typically underdetermined and has infinitely many solutions. Various forms of optimization can extract a "best" solution. One of the oldest is to select the one with minimal lscr<sub>2</sub> norm. It has been shown that in many applications a better choice is the minimal… (More)

- Ingrid Daubechies, Ronald A. DeVore, C. Sinan Güntürk, Vinay A. Vaishampayan
- IEEE Transactions on Information Theory
- 2006

This paper analyzes mathematically the effect of quantizer threshold imperfection commonly encountered in the circuit implementation of analog-to-digital (A/D) converters such as pulse code modulation (PCM) and sigma-delta (SigmaDelta) modulation. SigmaDelta modulation, which is based on coarse quantization of oversampled (redundant) samples of a signal,… (More)

- C. Sinan Güntürk, Mark Lammers, Alexander M. Powell, Rayan Saab, Özgür Yilmaz
- Foundations of Computational Mathematics
- 2013

Quantization of compressed sensing measurements is typically justified by the robust recovery results of Candès, Romberg and Tao, and of Donoho. These results guarantee that if a uniform quantizer of step size δ is used to quantize m measurements y = Φx of a k-sparse signal x ∈ R , where Φ satisfies the restricted isometry property, then the approximate… (More)

- Percy Deift, C. Sinan Güntürk, Felix Krahmer
- ArXiv
- 2010

Sigma-Delta modulation is a popular method for analog-to-digital conversion of bandlimited signals that employs coarse quantization coupled with oversampling. The standard mathematical model for the error analysis of the method measures the performance of a given scheme by the rate at which the associated reconstruction error decays as a function of the… (More)

- C. Sinan Güntürk, Nguyen T. Thao
- IEEE Trans. Information Theory
- 2004

- C. Sinan Güntürk, Jeffrey C. Lagarias, Vinay A. Vaishampayan
- IEEE Trans. Information Theory
- 2001

Sigma–delta modulation, a widely used method of analog-to-digital (A/D) signal conversion, is known to be robust to hardware imperfections, i.e., bit streams generated by slightly imprecise hardware components can be decoded comparably well. We formulate a model for robustness and give a rigorous analysis for single-loop sigma–delta modulation applied to… (More)

- C. SİNAN GÜNTÜRK
- 2003

This paper concerns fine analytical error estimates in analog-to-digital conversion of bandlimited functions using the method of sigma-delta modulation (also called Σ∆ quantization). This method has found widespread usage in practice due to several advantages in its implementation compared to conventional methods (see [1, 11]). A recent mathematical… (More)

- C. Sinan Güntürk, Alexander M. Powell, Rayan Saab, Özgür Yilmaz
- ArXiv
- 2010

Quantization of compressed sensing measurements is typically justified by the robust recovery results of Candès, Romberg and Tao, and of Donoho. These results guarantee that if a uniform quantizer of step size δ is used to quantize m measurements y = Φx of a k-sparse signal x ∈ RN , where Φ satisfies the restricted isometry property, then the approximate… (More)

- C. Sinan Güntürk
- 1999

A sigma-delta modulator converts a sequence of real numbers bounded by 1 into a digital sequence with entries +1 and 1 only. When the input sequence consists of samples of a bandlimited function, oversampled by a factor with respect to its Nyquist frequency, we prove that filtering the digital output with an appropriate kernel reproduces the original… (More)

- Hakan Caglar, C. Sinan Güntürk, Bülent Sankur, Emin Anarim
- IEEE Trans. Image Processing
- 1998

Two new design techniques for adaptive orthogonal block transforms based on vector quantization (VQ) codebooks are presented. Both techniques start from reference vectors that are adapted to the characteristics of the signal to be coded, while using different methods to create orthogonal bases. The resulting transforms represent a signal coding tool that… (More)