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Rick Chartrand, Kevin R. Vixie, Brendt Wohlberg and Erik M. Bollt, "A gradient descent solution to the Monge-Kantorovich problem", Appl. Math. Sci., vol. 3, no. 22, pp. 1071--1080, 2009


We present a new, simple, and elegant algorithm for computing the optimal mapping for the Monge-Kantorovich problem with quadratic cost. The method arises from a reformulation of the dual problem into an unconstrained minimization of a convex, continuous functional, for which the derivative can be explicitly found. The Monge-Kantorovich problem has applications in many fields; examples from image warping and medical imaging are shown.

BibTeX Entry

author = {Rick Chartrand and Kevin R. Vixie and Brendt Wohlberg and Erik M. Bollt},
title = {A gradient descent solution to the {M}onge-{K}antorovich problem},
year = {2009},
urlpdf = {},
journal = {Appl. Math. Sci.},
volume = {3},
number = {22},
pages = {1071--1080}