### 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 language | English |
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Pages (from-to) | 79-100 |

Number of pages | 22 |

Journal | Journal of Scientific Computing |

Volume | 77 |

Issue number | 1 |

DOIs | |

Publication status | Published - Oct 1 2018 |

Externally published | Yes |

### Fingerprint

### All Science Journal Classification (ASJC) codes

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

### Cite this

*Journal of Scientific Computing*,

*77*(1), 79-100. https://doi.org/10.1007/s10915-018-0696-8

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

Research output: Contribution to journal › Article

*Journal of Scientific Computing*, vol. 77, no. 1, pp. 79-100. https://doi.org/10.1007/s10915-018-0696-8

}

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

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.

UR - http://www.scopus.com/inward/record.url?scp=85044073530&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85044073530&partnerID=8YFLogxK

U2 - 10.1007/s10915-018-0696-8

DO - 10.1007/s10915-018-0696-8

M3 - Article

VL - 77

SP - 79

EP - 100

JO - Journal of Scientific Computing

JF - Journal of Scientific Computing

SN - 0885-7474

IS - 1

ER -