Echo-location is a broad approach to imaging and sensing that includes both man-made RADAR, LIDAR, SONAR and also animal navigation. However, full 3D information based on echo-location requires some form of scanning of the scene in order to provide the spatial location of the echo origin-points. Without this spatial information, imaging objects in 3D is a very challenging task as the inverse retrieval problem is strongly ill-posed. Here, we show that the temporal information encoded in the return echoes that are reflected multiple times within a scene is sufficient to faithfully render an image in 3D. Numerical modelling and an information theoretic perspective prove the concept and provide insight into the role of the multipath information. We experimentally demonstrate the concept by using both radio-frequency and acoustic waves for imaging individuals moving in a closed environment.
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