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{\large Malena I. Espanol \\
{\bf Multilevel approach for signal restoration problems with Toeplitz matrices.}}

Department of Mathematics \\ Tufts University \\
503 Boston Ave \\
Medford, MA 02155 \\
{\tt malena.espanol@tufts.edu} \\
Misha E. Kilmer
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We present a multilevel method for discrete ill-posed problems arising from the
discretization of Fredholm integral equations of the first kind. In
this method we use the Haar wavelets as restriction and prolongation
operators. The choice of the Haar wavelet operator has the advantage
of preserving matrix structure, such as Toeplitz, between grids, which
can be exploited to obtain faster solvers on each level. Finally,
we present results that indicate the promise of this approach on restoration of signals with edges.
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