\title{Kronecker Product Preconditioners in Image Restoration}

\author{Julie Kamm, James G. Nagy}

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\maketitle

Image restoration is the process of removing or minimizing degradations in an observed image. It is often modeled as a discrete ill-posed problem $g=Kf+n$, where $K$ is a large ill-conditioned matrix representing the blurring phenomena, $g$ is the observed image and $n$ denotes noise. Iterative methods, such as conjugate gradients, can be used to compute approximations to the true image $f$. Circulant matrices are typically used as preconditioners to accelerate convergence. In this talk we consider an alternative approach based on Kronecker product approximations. Theoretical results establish the optimality of the preconditioner, and numerical results using examples from astronomical imaging will be presented.

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