An Efficient Algorithm for Matrix-Valued and Vector-Valued Optimal Mass Transport
(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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- author
- Chen, Yongxin ; Haber, Eldad ; Yamamoto, Kaoru LU ; Georgiou, Tryphon T. and Tannenbaum, Allen
- organization
- publishing date
- 2018-03-16
- 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
- 2022-04-25 06:37:28
@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}},
keywords = {{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}},
doi = {{10.1007/s10915-018-0696-8}},
volume = {{77}},
year = {{2018}},
}