February 2014
Intermediate to advanced
300 pages
11h 15m
English
Content preview from Iterative Optimization in Inverse Problems
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250 Iterative Optimization in Inverse Problems
18.3.3 Iterative Reweighting
Let x denote the truth. We want each weight w
n
to be a good prior
estimate of the reciprocal of |x
n
|. Because we do not yet know x,wemay
take a sequential-optimization approach, beginning with weights w
0
n
> 0,
finding the PDFT solution using these weights, then using this PDFT so-
lution to get a (we hope!) better choice for the weights, and so on. This
sequential approach was successfully implemented in the early 1980’s by
Michael Fiddy and his students [127].
In [75], the same approach is taken, but with respect to the one-norm.
Since the one-norm still penalizes larger values ...
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