Kronecker Product Approximation for Three-Dimensional Imaging Applications

J. Nagy and M. Kilmer

We derive Kronecker product approximations, with the help of tensor decompositions, to construct approximations of severely ill-conditioned matrices that arise in three-dimensional image processing applications. We use the Kronecker product approximations to derive preconditioners for iterative regularization techniques; the resulting preconditioned algorithms allow us to restore three dimensional 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.