Kronecker Product Approximations for Image Restoration
with Reflexive Boundary Conditions
J. Nagy, M. Ng and L. Perrone
Many image processing applications require computing approximate
solutions of very large, ill-conditioned linear systems. Physical
assumptions of the imaging system usually mean that the matrices in
these linear systems have exploitable structure. The specific
structure depends on (usually simplifying) assumptions of the physical
model, and other considerations such as boundary conditions. When
reflexive (Neumann) boundary conditions are used, the coefficient
matrix is a combination of Toeplitz and Hankel matrices.
Kronecker products also occur, but this structure is
not obvious from measured data. In this paper we discuss a scheme for
computing a (possibly approximate) Kronecker product decomposition of
structured matrices in image processing, which extends previous work
\cite{KaNa00} by Kamm and Nagy to a wider class of image
restoration problems.