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In this paper, we propose a method to find the best Kronecker product approximationof the blurring operator which arises in three dimensional image restoration problems. We show thatthis problem can be reduced to a well known rank-1 approximation of the scaled three dimensionalpoint spread function (PSF) array, which is much smaller. This approximation can be used as apreconditioner in solving image restoration problems with iterative methods. The comparison ofthe approximation by the new scaled PSF array and approximation by the original PSF array that is used in [J. G. Nagy and M. E. Kilmer, IEEE Trans. Image Process., 15 (2006), pp. 604–613],confirms the performance of the new proposed approximation

Best Kronecker Product Approximation of The Blurring Operator in Three Dimensional Image Restoration Problems