Tikhonov regularization is the most popular general-purpose method
for regularization, a mathematical technique to suppress the effect
of noise in data, and uses much of the machinery of Hilbert space
theory. This book develops the theory of Tikhonov regularization
for a certain class of linear inverse problems which are defined on
Hilbert spaces. To explain why and how Tikhonov regularization
works, the singular value expansion for compact operators is
introduced. Tikhonov regularization with seminorms is also analyzed
and for this purpose, densely defined unbounded operators are
addressed and their basic properties presented. In addition, the
author provides readers with a quick but thorough review of Hilbert
space theory and a brief introduction to weak derivatives and
Sobolev spaces. Intended as an expository work for those interested
in inverse problems and Tikhonov regularization, including
graduates and researchers, the author presents the theory in an
engaging and straightforward style.
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