To save content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about saving content to .
To save content items to your Kindle, first ensure no-reply@cambridge.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
This chapter sets the stage for the study of algorithms used in the practical solution of the phase retrieval problem. It defines the types of maps used and many of the algorithms that will be considered in Chapters 7–10. Many of the concepts that arise in these chapters are introduced here as well.
Recovering the phase of the Fourier transform is a ubiquitous problem in imaging applications from astronomy to nanoscale X-ray diffraction imaging. Despite the efforts of a multitude of scientists, from astronomers to mathematicians, there is, as yet, no satisfactory theoretical or algorithmic solution to this class of problems. Written for mathematicians, physicists and engineers working in image analysis and reconstruction, this book introduces a conceptual, geometric framework for the analysis of these problems, leading to a deeper understanding of the essential, algorithmically independent, difficulty of their solutions. Using this framework, the book studies standard algorithms and a range of theoretical issues in phase retrieval and provides several new algorithms and approaches to this problem with the potential to improve the reconstructed images. The book is lavishly illustrated with the results of numerous numerical experiments that motivate the theoretical development and place it in the context of practical applications.
Experience a guided tour of the key information-theoretic principles that underpin the design of next-generation cellular systems with this invaluable reference. Written by experts in the field, the text encompasses principled theoretical guidelines for the design and performance analysis of network architectures, coding and modulation schemes, and communication protocols. Presenting an extensive overview of the most important ideas and topics necessary for the development of future wireless systems, as well as providing a detailed introduction to network information theory, this is the perfect tool for researchers and graduate students in the fields of information theory and wireless communications, as well as for practitioners in the telecommunications industry.