Inferring spatial scenes from their time-resolved multipath echoes

Is it fundamentally possible to reconstruct a 3D scene from a purely temporal measurement? We define a purely temporal measurement as being made by a wide-field single-pixel bucket detector, viewing a scene illuminated uniformly, without scanning. Reconstructing a 3D scene from such data is strongly ill-posed, as a signal arriving time t d may have originated from not only a single point, but rather from any point ( x,y,z ) on the surface of a spherical dome defined by ( ct / 2 d 2) = x 2 + y 2 + z 2 . Yet, recent research has tackled this problem using strong priors regarding a fixed background, learned by a machine learning model [1] . This research limited itself to single-path echoes or in other words, the first reflection of waves from a scene. On the other hand, attempts at using multipath echoes - that is, data that contains waves that are reflected several times in the scene - without machine learning, constrained the reconstruction problem to simple scenes of a sparse set of points, reconstructable up to Euclidean congruence [2] . In this work, we demonstrate that using machine learning, multipath echoes of a scene provide an information-rich temporal trace, enabling high fidelity reconstruction of complex 3D scenes.