C. Sinan Güntürk

Learn More
Given an mtimesN matrix Phi, with m&lt;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)
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)
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)
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)
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)
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)
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)
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)