Kronecker product approximation for preconditioning in three-dimensional imaging applications

Authors:
J. G. Nagy;M. E. Kilmer
Affiliations:
Dept. of Math. & Comput. Sci., Emory Univ., Atlanta, GA, USA;-
Venue:
IEEE Transactions on Image Processing
Year:
2006

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Abstract

We derive Kronecker product approximations, with the help of tensor decompositions, to construct approximations of severely ill-conditioned matrices that arise in three-dimensional (3-D) image processing applications. We use the Kronecker product approximations to derive preconditioners for iterative regularization techniques; the resulting preconditioned algorithms allow us to restore 3-D images in a computationally efficient manner. Through examples in microscopy and medical imaging, we show that the Kronecker approximation preconditioners provide a powerful tool that can be used to improve efficiency of iterative image restoration algorithms.