The round-trip contrast problem

The contrast problem in nuclear magnetic resonance imaging has been treated by a variety of recent works. In this process, the image is typically captured multiple times to filter noise from the image, and to do so the system must return to its initial state before repeating the experiment. A natural motivation is to perform this return trip as quickly as possible, in particular with live subjects. In this article we introduce and discuss preliminary results of this so-called return trip of the contrast problem. The tools of geometric optimal control theory have been effectively applied to the contrast problem, and they are similarly employed to this problem which shares many characteristics. The time-minimal transfer in the single-spin case and preliminary results in the two-spin case are presented.