Optimal mass transport is an important technique with numerous applications in econometrics, fluid dynamics,
automatic control, statistical physics, shape optimization, expert systems, and meteorology. Motivated by certain
problems in image registration and medical image visualization, in this note, we describe a simple gradient
descent methodology for computing the optimal <i>L<sup>2</sup></i> transport mapping which may be easily implemented using
a multiresolution scheme. We also indicate how the optimal transport map may be computed on the sphere. A
numerical example is presented illustrating our ideas.