Solving Large-Scale Inverse Problems Via Approximate Message Passing and Optimization
Author : Yanting Ma
Publisher :
Page : 169 pages
File Size : 46,69 MB
Release : 2017
Category :
ISBN :
Author : Yanting Ma
Publisher :
Page : 169 pages
File Size : 46,69 MB
Release : 2017
Category :
ISBN :
Author : Neal Parikh
Publisher : Now Pub
Page : 130 pages
File Size : 15,74 MB
Release : 2013-11
Category : Mathematics
ISBN : 9781601987167
Proximal Algorithms discusses proximal operators and proximal algorithms, and illustrates their applicability to standard and distributed convex optimization in general and many applications of recent interest in particular. Much like Newton's method is a standard tool for solving unconstrained smooth optimization problems of modest size, proximal algorithms can be viewed as an analogous tool for nonsmooth, constrained, large-scale, or distributed versions of these problems. They are very generally applicable, but are especially well-suited to problems of substantial recent interest involving large or high-dimensional datasets. Proximal methods sit at a higher level of abstraction than classical algorithms like Newton's method: the base operation is evaluating the proximal operator of a function, which itself involves solving a small convex optimization problem. These subproblems, which generalize the problem of projecting a point onto a convex set, often admit closed-form solutions or can be solved very quickly with standard or simple specialized methods. Proximal Algorithms discusses different interpretations of proximal operators and algorithms, looks at their connections to many other topics in optimization and applied mathematics, surveys some popular algorithms, and provides a large number of examples of proximal operators that commonly arise in practice.
Author : Stephen Boyd
Publisher : Now Publishers Inc
Page : 138 pages
File Size : 35,81 MB
Release : 2011
Category : Computers
ISBN : 160198460X
Surveys the theory and history of the alternating direction method of multipliers, and discusses its applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others.
Author : Mung Chiang
Publisher : Now Publishers Inc
Page : 172 pages
File Size : 12,38 MB
Release : 2005
Category : Computers
ISBN : 9781933019093
Recently Geometric Programming has been applied to study a variety of problems in the analysis and design of communication systems from information theory and queuing theory to signal processing and network protocols. Geometric Programming for Communication Systems begins its comprehensive treatment of the subject by providing an in-depth tutorial on the theory, algorithms, and modeling methods of Geometric Programming. It then gives a systematic survey of the applications of Geometric Programming to the study of communication systems. It collects in one place various published results in this area, which are currently scattered in several books and many research papers, as well as to date unpublished results. Geometric Programming for Communication Systems is intended for researchers and students who wish to have a comprehensive starting point for understanding the theory and applications of geometric programming in communication systems.
Author : Stephen P. Boyd
Publisher : Cambridge University Press
Page : 744 pages
File Size : 13,87 MB
Release : 2004-03-08
Category : Business & Economics
ISBN : 9780521833783
Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
Author : Jérôme Idier
Publisher : John Wiley & Sons
Page : 322 pages
File Size : 44,17 MB
Release : 2013-03-01
Category : Mathematics
ISBN : 111862369X
Many scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest from measurable data. Unfortunately, most inverse problems are ill-posed, which means that precise and stable solutions are not easy to devise. Regularization is the key concept to solve inverse problems. The goal of this book is to deal with inverse problems and regularized solutions using the Bayesian statistical tools, with a particular view to signal and image estimation. The first three chapters bring the theoretical notions that make it possible to cast inverse problems within a mathematical framework. The next three chapters address the fundamental inverse problem of deconvolution in a comprehensive manner. Chapters 7 and 8 deal with advanced statistical questions linked to image estimation. In the last five chapters, the main tools introduced in the previous chapters are put into a practical context in important applicative areas, such as astronomy or medical imaging.
Author : Per Christian Hansen
Publisher : SIAM
Page : 144 pages
File Size : 20,16 MB
Release : 2006-01-01
Category : Technology & Engineering
ISBN : 9780898718874
Describes the deblurring algorithms and techniques collectively known as spectral filtering methods, in which the singular value decomposition, or a similar decomposition with spectral properties, is used to introduce the necessary regularization or filtering in the reconstructed image. The concise MATLAB® implementations described in the book provide a template of techniques that can be used to restore blurred images from many applications.
Author : Christelle Guéret
Publisher : Twayne Publishers
Page : 349 pages
File Size : 11,94 MB
Release : 2002
Category : Linear programming
ISBN : 9780954350307
Author :
Publisher :
Page : 692 pages
File Size : 32,62 MB
Release : 1995
Category : Aeronautics
ISBN :
Author : Yonina C. Eldar
Publisher : Cambridge University Press
Page : 837 pages
File Size : 21,94 MB
Release : 2015-04-09
Category : Computers
ISBN : 1107003393
A comprehensive guide to sampling for engineers, covering the fundamental mathematical underpinnings together with practical engineering principles and applications.