The Limits of Resolution

ISBN-13: 9780367876869 / Angielski / Miękka / 2019 / 568 str.

Geoffrey de Villiers; E. Roy Pike

Opis

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 concep

Spis treści

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

O autorze

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.