A geometric approach to multi-view compressive imaging
- PDF / 690,868 Bytes
- 15 Pages / 595.28 x 793.7 pts Page_size
- 76 Downloads / 192 Views
RESEARCH
Open Access
A geometric approach to multi-view compressive imaging Jae Young Park1* and Michael B Wakin2
Abstract 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 single- and 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. 1. Introduction Armed with potentially limited communication and computational resources, designers of distributed imaging systems face increasing challenges in the quest to acquire, compress, and communicate ever richer and higher-resolution image ensembles. In this paper, we consider multiview 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 (CS) [1,2] encoding schemes wherein each sensor directly and independently compresses its image using a small number of randomized measurements (see Figure 1). CS is commonly intended for the encoding of a single signal, and a rich theory has been developed for signal recovery from incomplete measurements by exploiting the assumption that the signal obeys a sparse model. In this paper, we * Correspondence: [email protected] 1 Department of Electrical Engineering and Computer Science at the University of Michigan, Ann Arbor, MI, USA Full list of author information is available at the end of the article
address the problem of how to recover an ensemble of images from a collection of image-by-image random measu
Data Loading...
