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Compressed Sensing & Sparse Filtering

  • Avishy Y. Carmi
  • Lyudmila Mihaylova
  • Simon J. Godsill

Part of the Signals and Communication Technology book series (SCT)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Avishy Y. Carmi, Lyudmila S. Mihaylova, Simon J. Godsill
    Pages 1-23
  3. Thomas Blumensath
    Pages 25-75
  4. Irina Rish, Genady Grabarnik
    Pages 77-93
  5. N. Hao, L. Horesh, M. E. Kilmer
    Pages 123-148
  6. Hongjian Sun, Arumugam Nallanathan, Jing Jiang
    Pages 149-185
  7. G. Mileounis, N. Kalouptsidis
    Pages 187-235
  8. Aleksandr Y. Aravkin, James V. Burke, Gianluigi Pillonetto
    Pages 237-280
  9. Avishy Y. Carmi
    Pages 281-324
  10. Deniz Üstebay, Rui Castro, Mark Coates, Michael Rabbat
    Pages 325-355
  11. Namrata Vaswani, Wei Lu
    Pages 357-380
  12. Manohar Shamaiah, Haris Vikalo
    Pages 381-393
  13. Ivana Stojanović, Müjdat Çetin, W. Clem Karl
    Pages 395-421
  14. James Murphy, Simon Godsill
    Pages 423-453
  15. Tara N. Sainath, Dimitri Kanevsky, David Nahamoo, Bhuvana Ramabhadran, Stephen Wright
    Pages 455-502

About this book

Introduction

This book is aimed at presenting concepts, methods and algorithms ableto cope with undersampled and limited data. One such trend that recently gained popularity and to some extent revolutionised signal processing is compressed sensing. Compressed sensing builds upon the observation that many signals in nature are nearly sparse (or compressible, as they are normally referred to) in some domain, and consequently they can be reconstructed to within high accuracy from far fewer observations than traditionally held to be necessary.

 Apart from compressed sensing this book contains other related approaches. Each methodology has its own formalities for dealing with such problems. As an example, in the Bayesian approach, sparseness promoting priors such as Laplace and Cauchy are normally used for penalising improbable model variables, thus promoting low complexity solutions. Compressed sensing techniques and homotopy-type solutions, such as the LASSO, utilise l1-norm penalties for obtaining sparse solutions using fewer observations than conventionally needed. The book emphasizes on the role of sparsity as a machinery for promoting low complexity representations and likewise its connections to variable selection and dimensionality reduction in various engineering problems.

 This book is intended for researchers, academics and practitioners with interest in various aspects and applications of sparse signal processing.  

Keywords

Bayesian approach L1-norm penalties compressive sampling compressive sensing homotopy-type solutions LASSO penalising improbable model variables sparse manifold learning sub-Nyquist sampling rates underdetermined system of linear equations

Editors and affiliations

  • Avishy Y. Carmi
    • 1
  • Lyudmila Mihaylova
    • 2
  • Simon J. Godsill
    • 3
  1. 1.Department of Mechanical and Aerospace EngineeringNanyang Technical UniversitySingaporeSingapore
  2. 2.School of Computing and CommunicationsLancaster UniversityLancasterUnited Kingdom
  3. 3.Department of EngineeringUniversity of CambridgeCambridgeUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-38398-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 2014
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-642-38397-7
  • Online ISBN 978-3-642-38398-4
  • Series Print ISSN 1860-4862
  • Series Online ISSN 1860-4870
  • Buy this book on publisher's site
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