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Kronecker product approximations for image restoration with anti‐reflective boundary conditions
Author(s) -
Perrone Lisa
Publication year - 2006
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.458
Subject(s) - kronecker product , mathematics , kronecker delta , boundary value problem , boundary (topology) , image restoration , matrix (chemical analysis) , algorithm , image (mathematics) , product (mathematics) , function (biology) , mathematical analysis , image processing , computer science , geometry , computer vision , physics , quantum mechanics , materials science , composite material , evolutionary biology , biology
The anti‐reflective boundary condition for image restoration was recently introduced as a mathematically desirable alternative to other boundary conditions presently represented in the literature. It has been shown that, given a centrally symmetric point spread function (PSF), this boundary condition gives rise to a structured blurring matrix, a submatrix of which can be diagonalized by the discrete sine transform (DST), leading to an O ( n 2 log n ) solution algorithm for an image of size n × n . In this paper, we obtain a Kronecker product approximation of the general structured blurring matrix that arises under this boundary condition, regardless of symmetry properties of the PSF. We then demonstrate the usefulness and efficiency of our approximation in an SVD‐based restoration algorithm, the computational cost of which would otherwise be prohibitive. Copyright © 2005 John Wiley & Sons, Ltd.