TY - JOUR
T1 - An Efficient Algorithm for Matrix-Valued and Vector-Valued Optimal Mass Transport
AU - Chen, Yongxin
AU - Haber, Eldad
AU - Yamamoto, Kaoru
AU - Georgiou, Tryphon T.
AU - Tannenbaum, Allen
N1 - Funding Information:
Acknowledgements This project was supported by AFOSR Grants (FA9550-15-1-0045 and FA9550-17-1-0435), ARO Grant (W911NF-17-1-049), grants from the National Center for Research Resources (P41-RR-013218) and the National Institute of Biomedical Imaging and Bioengineering (P41-EB-015902), National Science Foundation (NSF), grants from National Institutes of Health (1U24CA18092401A1, R01-AG048769), grants from the Swedish Research Council through the LCCC Linnaeus Center, and the Breast Cancer Research Foundation.
Funding Information:
This project was supported by AFOSR Grants (FA9550-15-1-0045 and FA9550-17-1-0435), ARO Grant (W911NF-17-1-049), grants from the National Center for Research Resources (P41- RR-013218) and the National Institute of Biomedical Imaging and Bioengineering (P41-EB-015902), National Science Foundation (NSF), grants from National Institutes of Health (1U24CA18092401A1, R01-AG048769), grants from the Swedish Research Council through the LCCC Linnaeus Center, and the Breast Cancer Research Foundation. Kaoru Yamamoto is a member of the LCCC Linnaeus Center and the ELLIIT Excellence Center at Lund University.
Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2018/10/1
Y1 - 2018/10/1
N2 - We present an efficient algorithm for recent generalizations of optimal mass transport theory to matrix-valued and vector-valued densities. These generalizations lead to several applications including diffusion tensor imaging, color image processing, and multi-modality imaging. The algorithm is based on sequential quadratic programming. By approximating the Hessian of the cost and solving each iteration in an inexact manner, we are able to solve each iteration with relatively low cost while still maintaining a fast convergence rate. The core of the algorithm is solving a weighted Poisson equation, where different efficient preconditioners may be employed. We utilize incomplete Cholesky factorization, which yields an efficient and straightforward solver for our problem. Several illustrative examples are presented for both the matrix and vector-valued cases.
AB - We present an efficient algorithm for recent generalizations of optimal mass transport theory to matrix-valued and vector-valued densities. These generalizations lead to several applications including diffusion tensor imaging, color image processing, and multi-modality imaging. The algorithm is based on sequential quadratic programming. By approximating the Hessian of the cost and solving each iteration in an inexact manner, we are able to solve each iteration with relatively low cost while still maintaining a fast convergence rate. The core of the algorithm is solving a weighted Poisson equation, where different efficient preconditioners may be employed. We utilize incomplete Cholesky factorization, which yields an efficient and straightforward solver for our problem. Several illustrative examples are presented for both the matrix and vector-valued cases.
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U2 - 10.1007/s10915-018-0696-8
DO - 10.1007/s10915-018-0696-8
M3 - Article
AN - SCOPUS:85044073530
SN - 0885-7474
VL - 77
SP - 79
EP - 100
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
IS - 1
ER -