February 2014
Intermediate to advanced
300 pages
11h 15m
English
Content preview from Iterative Optimization in Inverse Problems
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118 Iterative Optimization in Inverse Problems
8.4 Regularization
In many remote-sensing applications the entries of the vector b are mea-
sured data and therefore noisy. At the same time, the matrix A describing
the sensing process may be a simplification of the actual situation. Com-
bined, the description Ax = b may not be precisely true. In such cases,
finding an exact solution, even if one exists, may not be desirable, and
regularization is adopted. Imposing constraints on the vector x may also
result in there not being a solution.
8.4.1 Norm-Constrained Least-Squares
To regularize the least-squares problem we can minimize not b−Ax
2
,
but, say,
f(
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