FRI Sensing: Sampling Images along Unknown Curves

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. 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, called FRI Sensing. Our key finding is that, even if we don't have any position knowledge of the moving sensors, it's still possible to reconstruct the sampling trajectory (up to a linear transformation and a shift), and then reconstruct an image that represents the physical sampling field under certain hypotheses. We further investigate the reconstruction hypotheses and propose novel algorithms that could make this 1D to 2D reconstruction feasible. Experiments show that the proposed approach retrieves the sampling image and trajectory accurately under the developed hypotheses. This method can be applied to geolocation localization applications, such as indoor localization and submarine navigation. Moreover, we show that the proposed algorithms have the potential to visualize the one-dimensional signal, which may not be sampled from a real 2D/3D physical field (e.g. speech and text signals), as a two- or three-dimensional image.