title: Kronecker product approximation for preconditioning in three-dimensional imaging applications.
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.
authors.affiliation: Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA. nagy@mathcs.emory.edu
authors.forename: James G
authors.initials: JG
authors.lastname: Nagy
authors.forename: Misha E
authors.initials: ME
authors.lastname: Kilmer
mesh_terms: D000465:Algorithms; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity