Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Notation
- Part One Machine Learning
- Part Two Optimal Recovery
- Part Three Compressive Sensing
- Executive Summary
- 14 Sparse Recovery from Linear Observations
- 15 The Complexity of Sparse Recovery
- 16 Low-Rank Recovery from Linear Observations
- 17 Sparse Recovery from One-Bit Observations
- 18 Group Testing
- Part Four Optimization
- Part Five Neural Networks
- Appendices
- References
- Index
15 - The Complexity of Sparse Recovery
from Part Three - Compressive Sensing
Published online by Cambridge University Press: 21 April 2022
- Frontmatter
- Dedication
- Contents
- Preface
- Notation
- Part One Machine Learning
- Part Two Optimal Recovery
- Part Three Compressive Sensing
- Executive Summary
- 14 Sparse Recovery from Linear Observations
- 15 The Complexity of Sparse Recovery
- 16 Low-Rank Recovery from Linear Observations
- 17 Sparse Recovery from One-Bit Observations
- 18 Group Testing
- Part Four Optimization
- Part Five Neural Networks
- Appendices
- References
- Index
Summary
This chapter is concerned with the number of linear observations enabling the standard compressive sensing problem to be solved in a stable way. The upper estimate derived from the previous chapter is matched by a lower estimate obtained by a combinatorial argument. A connection with the Gelfand width of ?1-balls is then drawn. Finally, it is explained why stability quantified in ?2 is irrelevant in the context of compressive sensing.
- Type
- Chapter
- Information
- Mathematical Pictures at a Data Science Exhibition , pp. 123 - 131Publisher: Cambridge University PressPrint publication year: 2022