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\title{Multigrid preconditioners for\\ total variation image deblurring}
\author{Tony F Chan \\
UCLA, USA \\ E-mail: chan@math.ucla.edu \\
{\small Co-authors: Raymond Chan, W.L. Wan and C.K. Wong}}
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\maketitle

Total variation regularization has become popular recently
for image denoising and deblurring, primarily due to its superior
edge preservation properties. In the solution of the deblurring problem,
the need for preconditioning the sum of an elliptic operator and
a convolution operator arises. Each of the two operators are ill-conditioned,
with the elliptic operator having highly varying and near singular coefficients
and the convolution operators corresponding to some common point spread
functions (e.g. atmospheric blur) also extremely ill-conditioned.
Constructing effective preconditioners for such operators appears to be
very difficult, although there has been some progress reported in the
literature. In this talk, we shall discuss some recent work of ours
on using multigrid methods for this problem.


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