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{\large Misha Kilmer \\
{\bf Preconditioners for Image Deblurring from Low-rank Tensor Approximations }}

Tufts University \\ 503 Boston Ave \\ Medford \\ MA 02155
\\
{\tt misha.kilmer@tufts.edu}\\
Carla Martin\end{center}


In this talk, we consider the construction of preconditioners for
two-dimensional image deblurring.
First, we make an approximation that allows us to model the blurring as a special
product between a third order tensor and a two-dimensional image.
Building on a new notion
of tensor SVD, we express the tensor as a sum of so called {\it matrix
outer products}. To build the preconditioner
with the appropriate level of noise filtering, we truncate the expansion.
The preconditioner is then defined by
computing the tensor left inverse of the truncated expansion. Some of the
computations can be interleaved
for greater processing efficiency. We will give preliminary results
illustrating the potential of this approach.


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