# Kronecker Product and SVD Approximations for
Separable Spatially Variant Blurs

** J. Kamm and J. Nagy **

In image restoration,
a separable, spatially variant blurring function has
the form * k(x,y;s,t) = k1(x,s)k2(y,t)*. If this kernel
is known, then discretizations lead to a blurring
matrix which is a Kronecker product of two matrices
of smaller dimension.
If *k* is not known precisely, such a discretization
is not possible.
In this paper we describe an interpolation scheme to construct a
Kronecker product approximation to the blurring matrix
from a set of observed point spread functions
for separable, or nearly separable, spatially variant
blurs. An approximate singular value decomposition is
then computed from this Kronecker factorization.