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Iterative Optimization in Inverse Problems (Hardcover)
Loot Price: R4,650
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Iterative Optimization in Inverse Problems (Hardcover)
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Expected to ship within 9 - 15 working days
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Iterative Optimization in Inverse Problems brings together a number
of important iterative algorithms for medical imaging,
optimization, and statistical estimation. It incorporates recent
work that has not appeared in other books and draws on the author's
considerable research in the field, including his recently
developed class of SUMMA algorithms. Related to sequential
unconstrained minimization methods, the SUMMA class includes a wide
range of iterative algorithms well known to researchers in various
areas, such as statistics and image processing. Organizing the
topics from general to more specific, the book first gives an
overview of sequential optimization, the subclasses of
auxiliary-function methods, and the SUMMA algorithms. The next
three chapters present particular examples in more detail,
including barrier- and penalty-function methods, proximal
minimization, and forward-backward splitting. The author also
focuses on fixed-point algorithms for operators on Euclidean space
and then extends the discussion to include distance measures other
than the usual Euclidean distance. In the final chapters, specific
problems illustrate the use of iterative methods previously
discussed. Most chapters contain exercises that introduce new ideas
and make the book suitable for self-study. Unifying a variety of
seemingly disparate algorithms, the book shows how to derive new
properties of algorithms by comparing known properties of other
algorithms. This unifying approach also helps researchers-from
statisticians working on parameter estimation to image scientists
processing scanning data to mathematicians involved in theoretical
and applied optimization-discover useful related algorithms in
areas outside of their expertise.
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