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

Yongxin Chen, Eldad Haber, Kaoru Yamamoto, Tryphon T. Georgiou, Allen Tannenbaum

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 straightforward solver for our problem. Several illustrative examples are presented for both the matrix and vector-valued cases.

Original languageEnglish
Pages (from-to)79-100
Number of pages22
JournalJournal of Scientific Computing
Volume77
Issue number1
DOIs
Publication statusPublished - Oct 1 2018
Externally publishedYes

Fingerprint

Optimal Transport
Mass Transport
Efficient Algorithms
Mass transfer
Color Image Processing
Imaging
Iteration
Cholesky factorisation
Multimodality
Transport Theory
Quadratic Programming
Poisson's equation
Color image processing
Preconditioner
Diffusion tensor imaging
Convergence Rate
Tensor
Quadratic programming
Poisson equation
Factorization

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Cite this

An Efficient Algorithm for Matrix-Valued and Vector-Valued Optimal Mass Transport. / Chen, Yongxin; Haber, Eldad; Yamamoto, Kaoru; Georgiou, Tryphon T.; Tannenbaum, Allen.

In: Journal of Scientific Computing, Vol. 77, No. 1, 01.10.2018, p. 79-100.

Research output: Contribution to journalArticle

Chen, Yongxin ; Haber, Eldad ; Yamamoto, Kaoru ; Georgiou, Tryphon T. ; Tannenbaum, Allen. / An Efficient Algorithm for Matrix-Valued and Vector-Valued Optimal Mass Transport. In: Journal of Scientific Computing. 2018 ; Vol. 77, No. 1. pp. 79-100.
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