While sensors have been widely used in various applications, an essential current trend of research consists of collecting and fusing the information that comes from many sensors. Among these researches, combing the position information together with sensor data is particularly popular and prevalent, such as wireless sensor network localization. In this paper, on the contrary, we would like to concentrate on a unique mobile sensor. Our goal is to unveil the multidimensional information entangled within a stream of one-dimensional data. This task is called FRI Sensing. Our key finding is that, even if we don't have any position information of the moving sensors, it's still possible to reconstruct the sampling trajectory (up to a linear transformation and a shift), and then reconstruct the image that represents the physical sampling field. We further investigate the reconstruction hypotheses, derive the sampling theorem of FRI Sensing and propose a novel algorithm that could make this 1D to 2D reconstruction feasible. Experiments validate our theory and show that the proposed approach retrieves the sampling image and trajectory accurately under the derived hypotheses. Moreover, we show that the proposed method has the potential to visualize the one-dimensional signal, which may not be sampled from a real 2D/3D physical field as a two- or three-dimensional image.

https://ieeexplore.ieee.org/document/8682618