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Sparse and Redundant Representations

2010-08-12 Mathematics
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Release : 2010-08-12
Genre : Mathematics
Kind : eBook
Book Rating : 118/5 ( reviews)

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Book Synopsis Sparse and Redundant Representations by : Michael Elad

Download or read book Sparse and Redundant Representations written by Michael Elad. This book was released on 2010-08-12. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Wavelet Tour of Signal Processing

1999-09-14 Computers
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Release : 1999-09-14
Genre : Computers
Kind : eBook
Book Rating : 839/5 ( reviews)

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Book Synopsis A Wavelet Tour of Signal Processing by : Stephane Mallat

Download or read book A Wavelet Tour of Signal Processing written by Stephane Mallat. This book was released on 1999-09-14. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and École Polytechnique in Paris. Provides a broad perspective on the principles and applications of transient signal processing with wavelets Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet Content is accessible on several level of complexity, depending on the individual reader's needs New to the Second Edition Optical flow calculation and video compression algorithms Image models with bounded variation functions Bayes and Minimax theories for signal estimation 200 pages rewritten and most illustrations redrawn More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics

Curves and Surfaces

2012-01-06 Computers
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Release : 2012-01-06
Genre : Computers
Kind : eBook
Book Rating : 137/5 ( reviews)

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Book Synopsis Curves and Surfaces by : Jean-Daniel Boissonnat

Download or read book Curves and Surfaces written by Jean-Daniel Boissonnat. This book was released on 2012-01-06. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Curves and Surfaces, held in Avignon, in June 2010. The conference had the overall theme: "Representation and Approximation of Curves and Surfaces and Applications". The 39 revised full papers presented together with 9 invited talks were carefully reviewed and selected from 114 talks presented at the conference. The topics addressed by the papers range from mathematical foundations to practical implementation on modern graphics processing units and address a wide area of topics such as computer-aided geometric design, computer graphics and visualisation, computational geometry and topology, geometry processing, image and signal processing, interpolation and smoothing, scattered data processing and learning theory and subdivision, wavelets and multi-resolution methods.

Sparse Data Representation: The Role of Redundancy in Data Processing

2005
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Release : 2005
Genre :
Kind : eBook
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Book Synopsis Sparse Data Representation: The Role of Redundancy in Data Processing by :

Download or read book Sparse Data Representation: The Role of Redundancy in Data Processing written by . This book was released on 2005. Available in PDF, EPUB and Kindle. Book excerpt: The last decade has seen a dramatic increase in computational power and sensor ubiquity, as well as an ever increasing demand for finer resolution in both scientific and geometric modeling. This has led to the creation of enormously large data sets with exquisite detail. However, these data sets will be useful only if we can process them efficiently, whether it be for storage, transmission, visual display, fast on-line graphical query, correlation, or registration against data from other modalities. Raw data sets are typically inaccessible and need to be transformed to more efficient representations for further processing. Several competing issues emerge. Sparsity is essential for efficient transmission, storage, and computation. Multiscale representations are critical to extract features at desired scales. Implementation in silicon leads to new issues of robustness in the face of computational error and imprecise circuit implementation. An emerging technology to address these issues utilizes redundant representations. High oversampling followed by coarse quantization is the preferred method for analog to digital conversion of signals. Sparse representation of images using redundant families of waveforms is effectively utilized in feature extraction and denoising. These redundant families can be frames, dictionaries, or libraries of bases. On the other hand, there is, at present, no compelling theory to explain the advantages of redundancy in image and signal processing. This program will convene leading experts from data representation into two workshops to describe the current understanding of the benefits of redundancy and to set forward a program for further research.

Sparse and Redundant Representations for Inverse Problems and Recognition

2010
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Release : 2010
Genre :
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Book Synopsis Sparse and Redundant Representations for Inverse Problems and Recognition by : Vishal M. Patel

Download or read book Sparse and Redundant Representations for Inverse Problems and Recognition written by Vishal M. Patel. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt:

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