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Published in:
An Invitation to Compressive Sensing Read chapter Read first chapter

2013 | OriginalPaper | Chapter

11. Instance Optimality and Quotient Property

Authors : Simon Foucart, Holger Rauhut

Published in: A Mathematical Introduction to Compressive Sensing

Publisher: Springer New York

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Abstract

This chapter introduces the notion of instance optimality. While uniform ℓ 1-instance optimality is a practical concept in compressive sensing, uniform ℓ 2-instance optimality is shown not to be. A new property, called quotient property, is then developed to analyze measurement–reconstruction schemes. This property of the measurement matrix, coupled with equality-constrained ℓ 1-minimization, guarantees robustness of the scheme under measurement errors as well as nonuniform ℓ 2-instance optimality. The quotient property is proved to hold with high probability for Gaussian matrices and, modulo a slight modification, for subgaussian matrices.

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previous chapter Gelfand Widths of ℓ1-Balls
next chapter Random Sampling in Bounded Orthonormal Systems
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Metadata
Title
Instance Optimality and Quotient Property
Authors
Simon Foucart
Holger Rauhut
Copyright Year
2013
Publisher
Springer New York
Book
A Mathematical Introduction to Compressive Sensing

Print ISBN: 978-0-8176-4947-0

Electronic ISBN: 978-0-8176-4948-7

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-0-8176-4948-7_11

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