A geometric approach to multi-view compressive imaging

In this paper, we consider multi-view imaging problems in which an ensemble of cameras collect images describing a common scene. To simplify the acquisition and encoding of these images, we study the effectiveness of non-collaborative compressive sensing encoding schemes wherein each sensor directly and independently compresses its image using randomized measurements. After these measurements and also perhaps the camera positions are transmitted to a central node, the key to an accurate reconstruction is to fully exploit the joint correlation among the signal ensemble. To capture such correlations, we propose a geometric modeling framework in which the image ensemble is treated as a sampling of points from a low-dimensional manifold in the ambient signal space. Building on results that guarantee stable embeddings of manifolds under random measurements, we propose a “manifold lifting” algorithm for recovering the ensemble that can operate even without knowledge of the camera positions. We divide our discussion into two scenarios, the near-field and farfield cases, and describe how the manifold lifting algorithm could be applied to these scenarios. At the end of this paper, we present an in-depth case study of a far-field imaging scenario, where the aim is to reconstruct an ensemble of satellite images taken from different positions with limited but overlapping fields of view. In this case study, we demonstrate the impressive power of random measurements to capture singleand multi-image structure without explicitly searching for it, as the randomized measurement encoding in conjunction with the proposed manifold lifting algorithm can even outperform image-by-image transform coding.