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Selçuk Journal
of
Applied Mathematics
Summer-Autumn, 2002
Volume 3
Number 2
Research Center
of
Applied Mathematics
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SJAM
Summer-Autumn 2002, Volume 3 - Number 2
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A
new optimal
order
preconditioner for
high-resolution
image
reconstruction with
multisensors |
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Thomas Huckle
and Jochen
Staudacher |
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Institut
für Informatik,
TU München,
Boltzmannstr. 3, 85748 Garching,
Germany
email :
huckle@in.tum.de ;
email:
staudacj@in.tum.de
Received: August
17, 2002
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Summary
This
paper is devoted
to the
problem of high-resolution
image
reconstruction with
multisensors: There
a high-resolution
image is
reconstructed from
four undersampled,
shifted, degraded
and noisy
low-resolution
images. Previously
R. Chan, T. Chan,
M. Ng and
their collaborators
had been proposing
very successful
fast cosine
transform based
preconditioners for
the arising
linear systems.On
the other
hand, no O(n)
preconditioners for
these sparse
problems had been
developed. We
present a simple
and effective
O(n) preconditioner
based on the
structure of the
linear systems:
The idea is
that the
system matrices
allow for a
helpful "analytic
factorization".
Various numerical
experiments
underline that
our preconditioner
leads in fact
to an efficient
optimal order
performance. |
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Key
words
sparse
linear systems,
preconditioned
conjugate gradients,
Kronecker products,
inverse problems,
Tikhonov
regularization, image
processing.
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2000 Mathematics
Subject
Classification : 65F10, 65F22, 65F50
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Article
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