Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Optimal transportation for electrical impedance tomography
HTML articles powered by AMS MathViewer

by Gang Bao and Yixuan Zhang;
Math. Comp. 93 (2024), 2361-2389
DOI: https://doi.org/10.1090/mcom/3919
Published electronically: November 13, 2023

Abstract:

This work establishes a framework for solving inverse boundary problems with the geodesic-based quadratic Wasserstein distance ($W_{2}$). A general form of the Fréchet gradient is systematically derived from the optimal transportation (OT) theory. In addition, a fast algorithm based on the new formulation of OT on $\mathbb {S}^{1}$ is developed to solve the corresponding optimal transport problem. The computational complexity of the algorithm is reduced to $O(N)$ from $O(N^{3})$ of the traditional method. Combining with the adjoint-state method, this framework provides a new computational approach for solving the challenging electrical impedance tomography problem. Numerical examples are presented to illustrate the effectiveness of our method.
References
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2020): 49Q20, 35R30, 65M32
  • Retrieve articles in all journals with MSC (2020): 49Q20, 35R30, 65M32
Bibliographic Information
  • Gang Bao
  • Affiliation: School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, People’s Republic of China
  • Email: baog@zju.edu.cn
  • Yixuan Zhang
  • Affiliation: School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, People’s Republic of China
  • ORCID: 0009-0004-0032-7916
  • Email: 11935010@zju.edu.cn
  • Received by editor(s): October 20, 2022
  • Received by editor(s) in revised form: August 2, 2023, and September 19, 2023
  • Published electronically: November 13, 2023
  • Additional Notes: This work was supported in part by National Natural Science Foundation of China (11621101; U21A20425) and a Key Laboratory of Zhejiang Province.
  • © Copyright 2023 American Mathematical Society
  • Journal: Math. Comp. 93 (2024), 2361-2389
  • MSC (2020): Primary 49Q20, 35R30, 65M32
  • DOI: https://doi.org/10.1090/mcom/3919
  • MathSciNet review: 4759378