Compressive Imaging Via One-Shot Measurements

One-shot measurement systems combine multiple frames of a signal such as a video into a single frame of the same dimensions. Each element (pixel) in the measured frame is a linear combination of the corresponding elements (pixels) in the combined frames. Such systems are a crucial part of various modern compressive imaging systems with applications ranging from high-speed videos to high-dimensional medical images. In this paper, employing ideas from compression-based compressed sensing, a new theoretical framework for such one-shot compressive imaging systems is proposed. This new framework enables us to show that it is possible to recover frames that are combined under the one-shot measurement paradigm. The number of frames that can be combined and later deconvolved is connected with the level of structured-ness of the original multi-frame signal. This theoretical analysis aims at filling the gap between existing practical compressive imaging systems and traditional compressed sensing theory developed for random and dense sensing matrices.