25 citations · 83 across the 10 of their papers we have counts for
10 papers
Approximation with one-bit polynomials in Bernstein form
C. Sinan Güntürk, Weilin Li
We prove various theorems on approximation using polynomials with integer coefficients in the Bernstein basis of any given order. In the extreme, we draw the coefficients from $\{…
Approximation of functions with one-bit neural networks
C. Sinan Güntürk, Weilin Li
The celebrated universal approximation theorems for neural networks roughly state that any reasonable function can be arbitrarily well-approximated by a network whose parameters ar…
Quantization for spectral super-resolution
C. Sinan Güntürk, Weilin Li
We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is…
Unrestricted iterations of relaxed projections in Hilbert space: Regularity, absolute convergence, and statistics of displacements
C. Sinan Güntürk, Nguyen T. Thao
Given a finite collection of closed linear subspaces of a real Hilbert space , let denote the orthogonal projection operator onto and $…
Convergence of the randomized Kaczmarz method for phase retrieval
Halyun Jeong, C. Sinan Güntürk
The classical Kaczmarz iteration and its randomized variants are popular tools for fast inversion of linear overdetermined systems. This method extends naturally to the setting of…
Distributed noise-shaping quantization: I. Beta duals of finite frames and near-optimal quantization of random measurements
Evan Chou, Sinan Güntürk
This paper introduces a new algorithm for the so-called "Analysis Problem" in quantization of finite frame representations which provides a near-optimal solution in the case of ran…
Sobolev Duals for Random Frames and Sigma-Delta Quantization of Compressed Sensing Measurements
S. Güntürk, A. Powell, R. Saab +1
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 u…
An Optimal Family of Exponentially Accurate One-Bit Sigma-Delta Quantization Schemes
Percy Deift, C. Sinan Güntürk, Felix Krahmer
Sigma-Delta modulation is a popular method for analog-to-digital conversion of bandlimited signals that employs coarse quantization coupled with oversampling. The standard mathemat…
The Golden Ratio Encoder
I. Daubechies, C. S. Güntürk, Y. Wang +1
This paper proposes a novel Nyquist-rate analog-to-digital (A/D) conversion algorithm which achieves exponential accuracy in the bit-rate despite using imperfect components. The pr…
Iteratively re-weighted least squares minimization for sparse recovery
Ingrid Daubechies, Ronald DeVore, Massimo Fornasier +1
We analyze an Iteratively Re-weighted Least Squares (IRLS) algorithm for promoting l1-minimization in sparse and compressible vector recovery. We prove its convergence and we estim…