This book brings together the concept of resolution, which limits what we can determine about our physical world, with linear inverse problems, with an emphasis on showcasing real examples and practical applications. The book focuses on methods for solving illposed problems that do not have unique stable solutions. After introducing basic concepts, the contents address problems with "continuous" data in detail before turning to cases of discrete data sets. As one of the unifying principles of the text, the authors explain how non-uniqueness is a feature of measurement problems in science where precision and resolution is essentially always limited by some kind of noise.
Autorentext
Geoffrey D de Villiers (M Inst P. C.Phys., FIMA, C.Math) is currently an honorary senior research fellow in the School of Electronic, Electrical and Systems Engineering at the University of Birmingham. He is an applied mathematician with over 30 years of experience in signal processing. His specialty is linear inverse problems with particular emphasis on singular-function methods and resolution enhancement. He has worked on a wide variety of practical inverse problems in photon correlation spectroscopy, radar, sonar, communications, seismology, antenna array design, broadband array processing, computational imaging and, currently, gravitational imaging.
E. Roy Pike FRS has been Clerk-Maxwell Professor for Theoretical Physics at King's College London, and head of its School of Physical Sciences and Engineering, and is currently Emeritus Professor of Physics.
Zusammenfassung
"e;This beautiful book can be read as a novel presenting carefully our quest to get more and more information from our observations and measurements. Its authors are particularly good at relating it."e; --Pierre C. Sabatier "e;This is a unique text - a labor of love pulling together for the first time the remarkably large array of mathematical and statistical techniques used for analysis of resolution in many systems of importance today - optical, acoustical, radar, etc I believe it will find widespread use and value."e; --Dr. Robert G.W. Brown, Chief Executive Officer, American Institute of Physics"e;The mix of physics and mathematics is a unique feature of this book which can be basic not only for PhD students but also for researchers in the area of computational imaging."e; --Mario Bertero, Professor, University of Geneva"e;a tour-de-force covering aspects of history, mathematical theory and practical applications. The authors provide a penetrating insight into the often confused topic of resolution and in doing offer a unifying approach to the subject that is applicable not only to traditional optical systems but also modern day, computer-based systems such as radar and RF communications."e; --Prof. Ian Proudler, Loughborough University"e;a 'must have' for anyone interested in imaging and the spatial resolution of images. This book provides detailed and very readable account of resolution in imaging and organizes the recent history of the subject in excellent fashion. I strongly recommend it."e; --Michael A.a Fiddy, Professor, University of North Carolina at CharlotteThis book brings together the concept of resolution, which limits what we can determine about our physical world, with the theory of linear inverse problems, emphasizing practical applications. The book focuses on methods for solving illposed problems that do not have unique stable solutions. After introducing basic concepts, the contents address problems with "e;continuous"e; data in detail before turning to cases of discrete data sets. As one of the unifying principles of the text, the authors explain how non-uniqueness is a feature of measurement problems in science where precision and resolution is essentially always limited by some kind of noise.
Inhalt
Early concepts of resolution. Modern concepts of resolution. Elementary functional analysis. Resolution and ill-posedness. Optimisation. Deterministic methods for linear inverse problems. Convolution equations and deterministic spectral analysis. Statistical methods and resolution. Statistical spectral analysis. Resolution in optical microscopy. Some further optical applications. Appendixes. The origin of spectacles. Set theory and mappings. Methods for finding the eigenvalue and singular-value decompositions. Topological spaces. Basic probability theory