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

Research output: Contribution to journalArticle

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.

Details

Authors
  • Yongxin Chen
  • Eldad Haber
  • Kaoru Yamamoto
  • Tryphon T. Georgiou
  • Allen Tannenbaum
Organisations
External organisations
  • Iowa State University
  • University of British Columbia
  • University of California, Irvine
  • Stony Brook University
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Computational Mathematics

Keywords

  • Matrix-valued data, Optimal mass transport, Quantum mechanics, Vector-valued data
Original languageEnglish
Pages (from-to)79-100
JournalJournal of Scientific Computing
Volume77
Issue number1
Early online date2018 Mar 16
Publication statusPublished - 2018
Publication categoryResearch
Peer-reviewedYes