Single-Pixel Imaging Of Dynamic Flows Using Neural Ode Regularization

Aleksei Sholokhov, Joshua Rapp, Saleh Nabi, Steven L. Brunton, J. Nathan Kutz, Hassan Mansour

Abstract: Single-pixel imaging is an efficient image acquisition process where light from a target scene is passed through a spatial light modulator and then projected onto a single photodiode with a high temporal acquisition rate. The scene reconstruction is achieved using computational methods that leverage prior assumptions on the scene structure. In this paper, we propose to model the structure of a dynamic spatio-temporal scene using a reduced-order model that is learned from training data examples. Specifically, by combining single-pixel imaging methods with a reduced-order model prior implemented as a neural ordinary differential equation, image sequence reconstruction can be accomplished with significantly reduced data requirements while maintaining performance levels on par with leading methods. We demonstrate superior reconstruction at low sampling rates for simulated trajectories governed by Burgers’ equation and turbulent plumes emulating gas leaks.