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Geometry of the Phase Retrieval Problem - Graveyard of Algorithms (Hardcover)
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Geometry of the Phase Retrieval Problem - Graveyard of Algorithms (Hardcover)
Series: Cambridge Monographs on Applied and Computational Mathematics
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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.
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