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An Efficient Algorithm for Matrix-Valued and Vector-Valued Optimal Mass Transport

Chen, Yongxin; Haber, Eldad; Yamamoto, Kaoru LU ; Georgiou, Tryphon T. and Tannenbaum, Allen (2018) In Journal of Scientific Computing 77(1). p.79-100
Abstract

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... (More)

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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Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Matrix-valued data, Optimal mass transport, Quantum mechanics, Vector-valued data
in
Journal of Scientific Computing
volume
77
issue
1
pages
79 - 100
publisher
Springer
external identifiers
  • scopus:85044073530
ISSN
0885-7474
DOI
10.1007/s10915-018-0696-8
language
English
LU publication?
yes
id
8915b9b9-caeb-4ecc-9cb5-f53146634279
date added to LUP
2018-04-03 15:41:41
date last changed
2019-01-14 12:51:50
@article{8915b9b9-caeb-4ecc-9cb5-f53146634279,
  abstract     = {<p>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.</p>},
  author       = {Chen, Yongxin and Haber, Eldad and Yamamoto, Kaoru and Georgiou, Tryphon T. and Tannenbaum, Allen},
  issn         = {0885-7474},
  keyword      = {Matrix-valued data,Optimal mass transport,Quantum mechanics,Vector-valued data},
  language     = {eng},
  month        = {03},
  number       = {1},
  pages        = {79--100},
  publisher    = {Springer},
  series       = {Journal of Scientific Computing},
  title        = {An Efficient Algorithm for Matrix-Valued and Vector-Valued Optimal Mass Transport},
  url          = {http://dx.doi.org/10.1007/s10915-018-0696-8},
  volume       = {77},
  year         = {2018},
}