The Sparse Fourier Transform. Haitham Hassanieh

Chapter 2

      10.1145/3166186.3166190 Chapter 3

      10.1145/3166186.3166191 Chapter 4

      10.1145/3166186.3166192 Chapter 5

      10.1145/3166186.3166193 Chapter 6

      10.1145/3166186.3166194 Chapter 7

      10.1145/3166186.3166195 Chapter 8

      10.1145/3166186.3166196 Chapter 9

      10.1145/3166186.3166197 Chapter 10

      10.1145/3166186.3166198 Chapter 11

      10.1145/3166186.3166199 Chapter 12

      10.1145/3166186.3166200 Appendices

      10.1145/3166186.3166201 References

      A publication in the ACM Books series, #19

      Editor in Chief: M. Tamer Özsu, University of Waterloo

      First Edition

      10 9 8 7 6 5 4 3 2 1

       To Maha and Nadima Hassanieh

       Contents

	Preface
Chapter 1	Introduction
	1.1 Sparse Fourier Transform Algorithms
	1.2 Applications of the Sparse Fourier Transform
	1.3 Book Overview
PART I	THEORY OF THE SPARSE FOURIER TRANSFORM
Chapter 2	Preliminaries
	2.1 Notation
	2.2 Basics
Chapter 3	Simple and Practical Algorithm
	3.1 Introduction
	3.2 Algorithm
Chapter 4	Optimizing Runtime Complexity
	4.1 Introduction
	4.2 Algorithm for the Exactly Sparse Case
	4.3 Algorithm for the General Case
	4.4 Extension to Two Dimensions
Chapter 5	Optimizing Sample Complexity
	5.1 Introduction
	5.2 Algorithm for the Exactly Sparse Case
	5.3 Algorithm for the General Case
Chapter 6	Numerical Evaluation
	6.1 Implementation
	6.2 Experimental Setup
	6.3 Numerical Results
PART II	APPLICATIONS OF THE SPARSE FOURIER TRANSFORM
Chapter 7	GHz-Wide Spectrum Sensing and Decoding
	7.1 Introduction
	7.2 Related Work
	7.3 BigBand
	7.4 Channel Estimation and Calibration
	7.5 Differential Sensing of Non-Sparse Spectrum
	7.6 A USRP-Based Implementation
	7.7 BigBand’s Spectrum Sensing Results
	7.8 BigBand’s Decoding Results
	7.9 D-BigBand’s Sensing Results
	7.10 Conclusion
Chapter 8	Faster GPS Synchronization
	8.1 Introduction
	8.2 GPS Primer
	8.3 QuickSync
	8.4 Theoretical Guarantees
	8.5 Doppler Shift and Frequency Offset
	8.6 Testing Environment
	8.7 Results
	8.8 Related Work
	8.9 Conclusion
Chapter 9	Light Field Reconstruction Using Continuous Fourier Sparsity
	9.1 Introduction
	9.2 Related Work
	9.3 Sparsity in the Discrete vs. Continuous Fourier Domain
	9.4 Light Field Notation
	9.5 Light Field Reconstruction Algorithm
	9.6 Experiments
	9.7 Results
	9.8 Discussion
	9.9 Conclusion
Chapter 10	Fast In-Vivo MRS Acquisition with Artifact Suppression
	10.1 Introduction
	10.2 MRS-SFT
	10.3 Methods
	10.4 MRS Results
	10.5 Conclusion
Chapter 11	Fast Multi-Dimensional NMR Acquisition and Processing
	11.1 Introduction
	11.2 Multi-Dimensional Sparse Fourier Transform
	11.3 Materials and Methods
	11.4 Results
	11.5 Discussion
	11.6 Conclusion
Chapter 12	Conclusion
	12.1 Future Directions
Appendix A	Proofs
Appendix B	The Optimality of the Exactly k-Sparse Algorithm 4.1
Appendix C	Lower Bound of the Sparse Fourier Transform