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.