Download or read book Sparse and Redundant Representations written by Michael Elad and published by Springer Science & Business Media. This book was released on 2010-08-12 with total page 376 pages. 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.

Download or read book A Wavelet Tour of Signal Processing written by Stephane Mallat and published by Elsevier. This book was released on 1999-09-14 with total page 663 pages. 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 ÉcolePolytechnique 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

Download or read book Sparse Image and Signal Processing written by Jean-Luc Starck and published by Cambridge University Press. This book was released on 2015-10-14 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents state-of-the-art sparse and multiscale image and signal processing with applications in astronomy, biology, MRI, media, and forensics.

Download or read book Mathematics in Image Processing written by Hong-Kai Zhao and published by American Mathematical Soc.. This book was released on 2013-06-12 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theme of the 2010 PCMI Summer School was Mathematics in Image Processing in a broad sense, including mathematical theory, analysis, computation algorithms and applications. In image processing, information needs to be processed, extracted and analyzed from visual content, such as photographs or videos. These demands include standard tasks such as compression and denoising, as well as high-level understanding and analysis, such as recognition and classification. Centered on the theme of mathematics in image processing, the summer school covered quite a wide spectrum of topics in this field. The summer school is particularly timely and exciting due to the very recent advances and developments in the mathematical theory and computational methods for sparse representation. This volume collects three self-contained lecture series. The topics are multi-resolution based wavelet frames and applications to image processing, sparse and redundant representation modeling of images and simulation of elasticity, biomechanics, and virtual surgery. Recent advances in image processing, compressed sensing and sparse representation are discussed.

Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.

Download or read book Sparse Modeling for Image and Vision Processing written by Julien Mairal and published by Now Publishers. This book was released on 2014-12-19 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sparse Modeling for Image and Vision Processing offers a self-contained view of sparse modeling for visual recognition and image processing. More specifically, it focuses on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.

Download or read book Independent Component Analysis and Blind Signal Separation written by Carlos G. Puntonet and published by Springer. This book was released on 2004-10-27 with total page 1287 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many situations found both in Nature and in human-built systems, a set of mixed signals is observed (frequently also with noise), and it is of great scientific and technological relevance to be able to isolate or separate them so that the information in each of the signals can be utilized. Blind source separation (BSS) research is one of the more interesting emerging fields now a days in the field of signal processing. It deals with the algorithms that allow the recovery of the original sources from a set of mixtures only. The adjective "blind" is applied because the purpose is to estimate the original sources without any a priori knowledge about either the sources or the mixing system. Most of the models employed in BSS assume the hypothesis about the independence of the original sources. Under this hypothesis, a BSS problem can be considered as a particular case of independent component analysis(ICA), a linear transformation technique that, starting from a multivariate representation of the data, minimizes the statistical dependence between the components of the representation. It can be claimed that most of the advances in ICA have been motivated by the search for solutions to the BSS problem and, the other way around, advances in ICA have been immediately applied to BSS. ICA and BSS algorithms start from a mixture model, whose parameters are estimated from the observed mixtures. Separation is achieved by applying the inverse mixture model to the observed signals(separating or unmixing model). Mixturem- els usually fall into three broad categories: instantaneous linear models, convolutive models and nonlinear models, the?rstone being the simplest but, in general, not near realistic applications. The development and test of the algorithms can be accomplished through synthetic data or with real-world data. Obviously, the most important aim(and most difficult) is the separation of real-world mixtures. BSS and ICA have strong relations also, apart from signal processing, with other fields such as statistics and artificial neural networks. As long as we can find a system that emits signals propagated through a mean, andthosesignalsarereceivedbyasetofsensorsandthereisaninterestinrecovering the original sources, we have a potential field of application for BSS and ICA. Inside that wide range of applications we can find, for instance: noise reduction applications, biomedical applications, audio systems, telecommunications, and many others. This volume comes out just 20 years after the first contributions in ICA and BSS 1 appeared . Therein after, the number of research groups working in ICA and BSS has been constantly growing, so that nowadays we can estimate that far more than 100 groups are researching in these fields. As proof of the recognition among the scientific community of ICA and BSS developments there have been numerous special sessions and special issues in several well- 1 J. Herault, B. Ans, "Circuits neuronaux à synapses modi?ables: décodage de messages composites para apprentissage non supervise", C.R. de l'Académie des Sciences, vol. 299, no. III-13,pp.525-528,1984

Download or read book Sparsity Methods for Systems and Control written by Masaaki Nagahara and published by . This book was released on 2020-09-30 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of sparsity has been attracting a lot of attention in the fields related not only to signal processing, machine learning, and statistics, but also systems and control. The method is known as compressed sensing, compressive sampling, sparse representation, or sparse modeling. More recently, the sparsity method has been applied to systems and control to design resource-aware control systems. This book gives a comprehensive guide to sparsity methods for systems and control, from standard sparsity methods in finite-dimensional vector spaces (Part I) to optimal control methods in infinite-dimensional function spaces (Part II). The primary objective of this book is to show how to use sparsity methods for several engineering problems. For this, the author provides MATLAB programs by which the reader can try sparsity methods for themselves. Readers will obtain a deep understanding of sparsity methods by running these MATLAB programs. Sparsity Methods for Systems and Control is suitable for graduate level university courses, though it should also be comprehendible to undergraduate students who have a basic knowledge of linear algebra and elementary calculus. Also, especially part II of the book should appeal to professional researchers and engineers who are interested in applying sparsity methods to systems and control.

Download or read book Handbook of Mathematical Methods in Imaging written by Otmar Scherzer and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Download or read book Dictionary Learning Algorithms and Applications written by Bogdan Dumitrescu and published by Springer. This book was released on 2018-04-16 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers all the relevant dictionary learning algorithms, presenting them in full detail and showing their distinct characteristics while also revealing the similarities. It gives implementation tricks that are often ignored but that are crucial for a successful program. Besides MOD, K-SVD, and other standard algorithms, it provides the significant dictionary learning problem variations, such as regularization, incoherence enforcing, finding an economical size, or learning adapted to specific problems like classification. Several types of dictionary structures are treated, including shift invariant; orthogonal blocks or factored dictionaries; and separable dictionaries for multidimensional signals. Nonlinear extensions such as kernel dictionary learning can also be found in the book. The discussion of all these dictionary types and algorithms is enriched with a thorough numerical comparison on several classic problems, thus showing the strengths and weaknesses of each algorithm. A few selected applications, related to classification, denoising and compression, complete the view on the capabilities of the presented dictionary learning algorithms. The book is accompanied by code for all algorithms and for reproducing most tables and figures. Presents all relevant dictionary learning algorithms - for the standard problem and its main variations - in detail and ready for implementation; Covers all dictionary structures that are meaningful in applications; Examines the numerical properties of the algorithms and shows how to choose the appropriate dictionary learning algorithm.

Download or read book Graph Representation Learning written by William L. William L. Hamilton and published by Springer Nature. This book was released on 2022-06-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph-structured data is ubiquitous throughout the natural and social sciences, from telecommunication networks to quantum chemistry. Building relational inductive biases into deep learning architectures is crucial for creating systems that can learn, reason, and generalize from this kind of data. Recent years have seen a surge in research on graph representation learning, including techniques for deep graph embeddings, generalizations of convolutional neural networks to graph-structured data, and neural message-passing approaches inspired by belief propagation. These advances in graph representation learning have led to new state-of-the-art results in numerous domains, including chemical synthesis, 3D vision, recommender systems, question answering, and social network analysis. This book provides a synthesis and overview of graph representation learning. It begins with a discussion of the goals of graph representation learning as well as key methodological foundations in graph theory and network analysis. Following this, the book introduces and reviews methods for learning node embeddings, including random-walk-based methods and applications to knowledge graphs. It then provides a technical synthesis and introduction to the highly successful graph neural network (GNN) formalism, which has become a dominant and fast-growing paradigm for deep learning with graph data. The book concludes with a synthesis of recent advancements in deep generative models for graphs—a nascent but quickly growing subset of graph representation learning.

Download or read book Algorithmic Aspects of Machine Learning written by Ankur Moitra and published by Cambridge University Press. This book was released on 2018-09-27 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces cutting-edge research on machine learning theory and practice, providing an accessible, modern algorithmic toolkit.

Download or read book Sparse representation of visual data for compression and compressed sensing written by Ehsan Miandji and published by Linköping University Electronic Press. This book was released on 2018-11-23 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ongoing advances in computational photography have introduced a range of new imaging techniques for capturing multidimensional visual data such as light fields, BRDFs, BTFs, and more. A key challenge inherent to such imaging techniques is the large amount of high dimensional visual data that is produced, often requiring GBs, or even TBs, of storage. Moreover, the utilization of these datasets in real time applications poses many difficulties due to the large memory footprint. Furthermore, the acquisition of large-scale visual data is very challenging and expensive in most cases. This thesis makes several contributions with regards to acquisition, compression, and real time rendering of high dimensional visual data in computer graphics and imaging applications. Contributions of this thesis reside on the strong foundation of sparse representations. Numerous applications are presented that utilize sparse representations for compression and compressed sensing of visual data. Specifically, we present a single sensor light field camera design, a compressive rendering method, a real time precomputed photorealistic rendering technique, light field (video) compression and real time rendering, compressive BRDF capture, and more. Another key contribution of this thesis is a general framework for compression and compressed sensing of visual data, regardless of the dimensionality. As a result, any type of discrete visual data with arbitrary dimensionality can be captured, compressed, and rendered in real time. This thesis makes two theoretical contributions. In particular, uniqueness conditions for recovering a sparse signal under an ensemble of multidimensional dictionaries is presented. The theoretical results discussed here are useful for designing efficient capturing devices for multidimensional visual data. Moreover, we derive the probability of successful recovery of a noisy sparse signal using OMP, one of the most widely used algorithms for solving compressed sensing problems.

Download or read book A Mathematical Introduction to Compressive Sensing written by Simon Foucart and published by Springer Science & Business Media. This book was released on 2013-08-13 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing. Based on the premise that data acquisition and compression can be performed simultaneously, compressive sensing finds applications in imaging, signal processing, and many other domains. In the areas of applied mathematics, electrical engineering, and theoretical computer science, an explosion of research activity has already followed the theoretical results that highlighted the efficiency of the basic principles. The elegant ideas behind these principles are also of independent interest to pure mathematicians. A Mathematical Introduction to Compressive Sensing gives a detailed account of the core theory upon which the field is build. With only moderate prerequisites, it is an excellent textbook for graduate courses in mathematics, engineering, and computer science. It also serves as a reliable resource for practitioners and researchers in these disciplines who want to acquire a careful understanding of the subject. A Mathematical Introduction to Compressive Sensing uses a mathematical perspective to present the core of the theory underlying compressive sensing.

Download or read book Computer Vision ECCV 2012 written by Andrew Fitzgibbon and published by Springer. This book was released on 2012-09-26 with total page 909 pages. Available in PDF, EPUB and Kindle. Book excerpt: The seven-volume set comprising LNCS volumes 7572-7578 constitutes the refereed proceedings of the 12th European Conference on Computer Vision, ECCV 2012, held in Florence, Italy, in October 2012. The 408 revised papers presented were carefully reviewed and selected from 1437 submissions. The papers are organized in topical sections on geometry, 2D and 3D shapes, 3D reconstruction, visual recognition and classification, visual features and image matching, visual monitoring: action and activities, models, optimisation, learning, visual tracking and image registration, photometry: lighting and colour, and image segmentation.

Download or read book Sparse Representations for Radar with MATLAB Examples written by Peter Knee and published by Morgan & Claypool Publishers. This book was released on 2012 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the field of sparse representations is relatively new, research activities in academic and industrial research labs are already producing encouraging results. The sparse signal or parameter model motivated several researchers and practitioners to explore high complexity/wide bandwidth applications such as Digital TV, MRI processing, and certain defense applications. The potential signal processing advancements in this area may influence radar technologies. This book presents the basic mathematical concepts along with a number of useful MATLAB(R) examples to emphasize the practical implementations both inside and outside the radar field.

Download or read book An Introduction to Sparse Stochastic Processes written by Michael Unser and published by Cambridge University Press. This book was released on 2014-08-21 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed guide to sparsity, providing a description of their transform-domain statistics and applying the models to practical algorithms.