DocumentCode :
827434
Title :
Kronecker product approximation for preconditioning in three-dimensional imaging applications
Author :
Nagy, James G. ; Kilmer, Misha E.
Author_Institution :
Dept. of Math. & Comput. Sci., Emory Univ., Atlanta, GA, USA
Volume :
15
Issue :
3
fYear :
2006
fDate :
3/1/2006 12:00:00 AM
Firstpage :
604
Lastpage :
613
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.
Keywords :
image restoration; iterative methods; medical image processing; microscopy; Kronecker product approximation; image processing; iterative image restoration algorithms; iterative regularization techniques; tensor decomposition; three-dimensional imaging applications; Approximation algorithms; Biomedical imaging; Image processing; Image restoration; Integral equations; Iterative algorithms; Matrix decomposition; Microscopy; Singular value decomposition; Tensile stress; Image restoration; Kronecker products; iterative methods; orthogonal tensor decomposition; preconditioning; singular value decomposition (SVD); Algorithms; Image Enhancement; Image Interpretation, Computer-Assisted; Imaging, Three-Dimensional; Information Storage and Retrieval; Reproducibility of Results; Sensitivity and Specificity;
fLanguage :
English
Journal_Title :
Image Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1057-7149
Type :
jour
DOI :
10.1109/TIP.2005.863112
Filename :
1593664
Link To Document :
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