Kronecker Products in Image Restoration

James G. Nagy
Emory University

Image restoration is the process of minimizing or removing degradation from an observed image, which may be distorted by such things as blurring and noise. Such problems arise in applications ranging from microscopy to astronomy. Computational methods for restoring the image require solving large, very ill-conditioned linear
systems. The structure of the "blurring" matrix determines whether it is feasible to use matrix factorizations, or whether iterative methods are more appropriate for solving the linear systems.

In this talk we describe some aspects of image restoration algorithms, and show that the blurring matrix can often be represented in terms of Kronecker products. We also show how to exploit the Kronecker product structure to improve computational efficiency. Examples from various applications will be presented.

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