Journal ArticleDOI
Sigma-delta (/spl Sigma//spl Delta/) quantization and finite frames
TLDR
It is shown that /spl Sigma//spl Delta/ quantization of a unit-norm finite frame expansion in /spl Ropf//sup d/ achieves approximation error, and one is able to bound the mean squared error (MSE) by an order of 1/N/sup 2/.Abstract:
The K-level Sigma-Delta (/spl Sigma//spl Delta/) scheme with step size /spl delta/ is introduced as a technique for quantizing finite frame expansions for /spl Ropf//sup d/. Error estimates for various quantized frame expansions are derived, and, in particular, it is shown that /spl Sigma//spl Delta/ quantization of a unit-norm finite frame expansion in /spl Ropf//sup d/ achieves approximation error where N is the frame size, and the frame variation /spl sigma/(F,p) is a quantity which reflects the dependence of the /spl Sigma//spl Delta/ scheme on the frame. Here /spl par//spl middot//spl par/ is the d-dimensional Euclidean 2-norm. Lower bounds and refined upper bounds are derived for certain specific cases. As a direct consequence of these error bounds one is able to bound the mean squared error (MSE) by an order of 1/N/sup 2/. When dealing with sufficiently redundant frame expansions, this represents a significant improvement over classical pulse-code modulation (PCM) quantization, which only has MSE of order 1/N under certain nonrigorous statistical assumptions. /spl Sigma//spl Delta/ also achieves the optimal MSE order for PCM with consistent reconstruction.read more
Citations
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Journal ArticleDOI
Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors
TL;DR: This paper investigates an alternative CS approach that shifts the emphasis from the sampling rate to the number of bits per measurement, and introduces the binary iterative hard thresholding algorithm for signal reconstruction from 1-bit measurements that offers state-of-the-art performance.
Posted Content
Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors
TL;DR: In this paper, the authors consider the case of 1-bit CS measurements and provide a lower bound on the best achievable reconstruction error, and show that the same class of matrices that provide almost optimal noiseless performance also enable a robust mapping.
Journal ArticleDOI
Life Beyond Bases: The Advent of Frames (Part II)
Jelena Kovacevic,Amina Chebira +1 more
TL;DR: This part covers a large number of known frame families (harmonic tight frames, equiangular frames, unit-norm tight frame, Gabor frames, cosine-modulated frames, double-density frames, multidimensional frames, filter bank frame) as well as those applications where frames made a difference.
Journal ArticleDOI
Fusion frames and distributed processing
TL;DR: In this paper, the authors studied the robustness of fusion frame systems and proposed a weighted and distributed processing technique for fusion frames, which is a natural fit to distributed processing systems such as sensor networks, but also an efficient scheme for parallel processing of very large frame systems.
Book
An Introduction to Frames
Jelena Kovacevic,Amina Chebira +1 more
TL;DR: This survey gives an introduction to redundant signal representations called frames, which have recently emerged as yet another powerful tool in the signal processing toolbox and have become popular through use in numerous applications.
References
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Book
An introduction to frames and Riesz bases
TL;DR: In this article, a generalized Shift-Invariant Systems in L2(Rd) is proposed for Gabor Frames in L 2(Z),L 2(0,L),CL.
Book
Understanding Delta-Sigma Data Converters
TL;DR: This chapter discusses the design and simulation of delta-sigma modulator systems, and some of the considerations for implementation considerations for [Delta][Sigma] ADCs.
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