Sparse and Redundant Representations

1. Front Matter

   Pages i-xx

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2. Sparse and Redundant Representations – Theoretical and Numerical Foundations

   1. Front Matter

      Pages 1-1

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   2. Prologue

      • Michael Elad

      Pages 3-15

   3. Uniqueness and Uncertainty

      • Michael Elad

      Pages 17-33

   4. Pursuit Algorithms – Practice

      • Michael Elad

      Pages 35-54

   5. Pursuit Algorithms – Guarantees

      • Michael Elad

      Pages 55-77

   6. From Exact to Approximate Solutions

      • Michael Elad

      Pages 79-109

   7. Iterative-Shrinkage Algorithms

      • Michael Elad

      Pages 111-136

   8. Towards Average PerformanceAnalysis

      • Michael Elad

      Pages 137-151

   9. The Dantzig-Selector Algorithm

      • Michael Elad

      Pages 153-166

3. From Theory to Practice – Signal and Image Processing Applications

   1. Front Matter

      Pages 167-167

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   2. Sparsity-Seeking Methods in Signal Processing

      • Michael Elad

      Pages 169-184

   3. Image Deblurring – A Case Study

      • Michael Elad

      Pages 185-200

   4. MAP versus MMSE Estimation

      • Michael Elad

      Pages 201-225

   5. The Quest for a Dictionary

      • Michael Elad

      Pages 227-246

   6. Image Compression – Facial Images

      • Michael Elad

      Pages 247-271

   7. Image Denoising

      • Michael Elad

      Pages 273-307

   8. Other Applications

      • Michael Elad

      Pages 309-357

   9. Epilogue

      • Michael Elad

      Pages 359-361

4. Back Matter

   Pages 363-376

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A long long time ago, echoing philosophical and aesthetic principles that existed since antiquity, William of Ockham enounced the principle of parsimony, better known today as Ockham’s razor: “Entities should not be multiplied without neces sity. ” This principle enabled scientists to select the ”best” physical laws and theories to explain the workings of the Universe and continued to guide scienti?c research, leadingtobeautifulresultsliketheminimaldescriptionlength approachtostatistical inference and the related Kolmogorov complexity approach to pattern recognition. However, notions of complexity and description length are subjective concepts anddependonthelanguage“spoken”whenpresentingideasandresults. The?eldof sparse representations, that recently underwent a Big Bang like expansion, explic itly deals with the Yin Yang interplay between the parsimony of descriptions and the “language” or “dictionary” used in them, and it became an extremely exciting area of investigation. It already yielded a rich crop of mathematically pleasing, deep and beautiful results that quickly translated into a wealth of practical engineering applications. You are holding in your hands the ?rst guide book to Sparseland, and I am sure you’ll ?nd in it both familiar and new landscapes to see and admire, as well as ex cellent pointers that will help you ?nd further valuable treasures. Enjoy the journey to Sparseland! Haifa, Israel, December 2009 Alfred M. Bruckstein vii Preface This book was originally written to serve as the material for an advanced one semester (fourteen 2 hour lectures) graduate course for engineering students at the Technion, Israel.

• algorithms
• compression
• denoising
• extrapolation
• image processing
• interpolation
• restoration
• sampling
• seperation
• signal processing

From the reviews:

“This book approaches sparse and redundant representations from an engineering perspective and emphasizes their use as a signal modeling tool and their application in image and signal processing. … This book is well suited to practitioners in the signals and image processing community … . The public availability of the source code used in the numerical experiments throughout the book could help students make the transition from theory to practice and allow them to get hands-on experience with the inner workings of the various algorithms.”­­­ (Ewout van den Berg, SIAM Review, Vol. 53 (4), 2011)

“The concept of sparse representations for signals and images is explored in the book under review. … The book offers an important and organized view of this field, setting the foundations of the future research. … The presented book is written to serve as the material for an advanced one-semester graduate course for engineering students. It will be of interest for all specialists working in the area of sparse and redundant representations application in signal and image processing.” (Tzvetan Semerdjiev, Zentralblatt MATH, Vol. 1211, 2011)

• The Computer Science Department, Technion: Israel Institute of Technology, Haifa, Israel

  Michael Elad

Michael Elad has been working at The Technion in Haifa, Israel, since 2003 and is currently an Associate Professor. He is one of the leaders in the field of sparse representations. He does prolific research in mathematical signal processing with more than 60 publications in top ranked journals. He is very well recognized and respected in the scientific community.

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