Sparse and Redundant Representations

From Theory to Applications in Signal and Image Processing

Häftad, Engelska, 2014

AvMichael Elad

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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 alreadyyielded 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.

Produktinformation

Utgivningsdatum2014-10-20
Mått156 x 234 x 21 mm
Vikt554 g
FormatHäftad
SpråkEngelska
Antal sidor376
Upplaga2010
FörlagSpringer-Verlag New York Inc.
ISBN9781489982452

Tillhör följande kategorier

Sparse and Redundant Representations – Theoretical and Numerical Foundations.- Prologue.- Uniqueness and Uncertainty.- Pursuit Algorithms – Practice.- Pursuit Algorithms – Guarantees.- From Exact to Approximate Solutions.- Iterative-Shrinkage Algorithms.- Towards Average PerformanceAnalysis.- The Dantzig-Selector Algorithm.- From Theory to Practice – Signal and Image Processing Applications.- Sparsity-Seeking Methods in Signal Processing.- Image Deblurring – A Case Study.- MAP versus MMSE Estimation.- The Quest for a Dictionary.- Image Compression – Facial Images.- Image Denoising.- Other Applications.- Epilogue.

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)