Coherence Statistics of Structured Random Ensembles and Support Detection Bounds for OMP

A structured random matrix ensemble that maintains constant modulus entries and unit-norm columns, often called a random phase-rotated (RPR) matrix, is considered in this paper. We analyze the coherence statistics of RPR measurement matrices and apply them to acquire probabilistic performance guaran...

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Bibliographic Details
Published in:arXiv.org 2019-09
Main Authors: Duan, Qiyou, Kim, Taejoon, Lin, Dai, Perrins, Erik
Format: Article
Language:English
Subjects:
Coherence
Columns (structural)
Computer simulation
Online Access:Get full text
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Summary:A structured random matrix ensemble that maintains constant modulus entries and unit-norm columns, often called a random phase-rotated (RPR) matrix, is considered in this paper. We analyze the coherence statistics of RPR measurement matrices and apply them to acquire probabilistic performance guarantees of orthogonal matching pursuit (OMP) for support detection (SD). It is revealed via numerical simulations that the SD performance guarantee provides a tight characterization, especially when the signal is sparse.
ISSN:2331-8422
DOI:10.48550/arxiv.1909.07616