High-order low-bit Sigma-Delta quantization for fusion frames

被引：0

作者：

Gao, Zhen ^{[1
]}

Krahmer, Felix ^{[2
]}

Powell, Alexander M. ^{[1
]}

机构：

[1] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

[2] Tech Univ Munich, Res Unit M15, Dept Math, D-85748 Munich, Germany

来源：

ANALYSIS AND APPLICATIONS | 2021年 / 19卷 / 01期

基金：

美国国家科学基金会;

关键词：

Fusion frames; Sigma-Delta quantization; sensor networks; COARSE QUANTIZATION; CONVEX DYNAMICS; MODULATORS; BOUNDS; FAMILY;

D O I：

10.1142/S0219530520400096

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct high-order low-bit Sigma-Delta (Sigma Delta) quantizers for the vector-valued setting of fusion frames. We prove that these Sigma Delta quantizers can be stably implemented to quantize fusion frame measurements on subspaces Wn using log(2)(dim(W-n) + 1) bits per measurement. Signal reconstruction is performed using a version of Sobolev duals for fusion frames, and numerical experiments are given to validate the overall performance.

引用

页码：1 / 20

页数：20

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