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The Quest for Optimal Sampling: Computationally Efficient, Structure-Exploiting Measurements for Compressed Sensing

  • Ben AdcockEmail author
  • Anders C. Hansen
  • Bogdan Roman
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

An intriguing phenomenon in many instances of compressed sensing is that the reconstruction quality is governed not just by the overall sparsity of the object to recover, but also on its structure. This chapter is about understanding this phenomenon, and demonstrating how it can be fruitfully exploited by the design of suitable sampling strategies in order to outperform more standard compressed sensing techniques based on random matrices.

Keywords

Wavelet Coefficient Haar Wavelet Reconstruction Quality Restrict Isometry Property Orthonormal Wavelet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The authors thank Andy Ellison from Boston University Medical School for kindly providing the MRI fruit image, and General Electric Healthcare for kindly providing the brain MRI image. BA acknowledges support from the NSF DMS grant 1318894. ACH acknowledges support from a Royal Society University Research Fellowship. ACH and BR acknowledge the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/L003457/1.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsSimon Fraser UniversityBurnabyCanada
  2. 2.DAMTP, Centre for Mathematical SciencesUniversity of CambridgeCambridgeUK

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