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

Zhen Gao; Felix Krahmer; Alexander M. Powell

doi:10.1142/S0219530520400096

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

Zhen Gao, Felix Krahmer, Alexander M. Powell

Associate Professorship of Optimization and Data Analysis

Vanderbilt University

Research output: Contribution to journal › Article › peer-review

Abstract

We construct high-order low-bit Sigma-Delta (σΔ) quantizers for the vector-valued setting of fusion frames. We prove that these σΔ quantizers can be stably implemented to quantize fusion frame measurements on subspaces Wn using log2(dim(Wn) + 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.

Original language	English
Pages (from-to)	1-20
Number of pages	20
Journal	Analysis and Applications
Volume	19
Issue number	1
DOIs	https://doi.org/10.1142/S0219530520400096
State	Published - Jan 2021

Keywords

Fusion frames
Sigma-Delta quantization
sensor networks

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10.1142/S0219530520400096

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abstract = "We construct high-order low-bit Sigma-Delta (σΔ) quantizers for the vector-valued setting of fusion frames. We prove that these σΔ quantizers can be stably implemented to quantize fusion frame measurements on subspaces Wn using log2(dim(Wn) + 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.",

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

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Keywords

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