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Sparse and Redundant Representations

From Theory to Applications in Signal and Image Processing

By Michael Elad

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This book introduces sparse and redundant representations with a focus on applications in signal and image processing. It details mathematical modeling for signal sources along with how to use the model for tasks such as denoising, restoration and separation.

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  • ISBN13: 978-1-4419-7010-7
  • 396 Pages
  • Publication Date: August 12, 2010
  • Available eBook Formats: PDF
Full Description
This textbook introduces sparse and redundant representations with a focus on applications in signal and image processing. The theoretical and numerical foundations are tackled before the applications are discussed. Mathematical modeling for signal sources is discussed along with how to use the proper model for tasks such as denoising, restoration, separation, interpolation and extrapolation, compression, sampling, analysis and synthesis, detection, recognition, and more. The presentation is elegant and engaging. Sparse and Redundant Representations is intended for graduate students in applied mathematics and electrical engineering, as well as applied mathematicians, engineers, and researchers who are active in the fields of signal and image processing.
Table of Contents

Table of Contents

  1. Preface.
  2. Part I. Theoretical and Numerical Foundations.
  3. 1. Introduction.
  4. 2. Uniqueness and Uncertainty.
  5. 3. Pursuit Algorithms
  6. Practice.
  7. 4. Pursuit Algorithms
  8. Guarantees.
  9. 5. From Exact to Approximate Solution.
  10. 6. Iterated Shrinkage Algorithms.
  11. 7.Towards Average Performance Analysis.
  12. 8. The Danzig Selector Algorithm.
  13. Part II. Signal and Image Processing Applications.
  14. 9. Sparsity
  15. Seeking Methods in Signal Processing.
  16. 10. Image Deblurring
  17. A Case Study.
  18. 11. MAP versus MMSE Estimation.
  19. 12. The Quest For a Dictionary.
  20. 13. Image Compression
  21. Facial Images.
  22. 14. Image Denoising.
  23. 15. Other Applications.
  24. 16. Concluding Remarks.
  25. Bibliography.
  26. Index.

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