Compressive imaging via one-shot measurements

: One-shot measurement systems combine multiple frames in 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 reconstruct frames that are combined under the one-shot measurement paradigm. The number of frames that can be combined and later deconvoluted is connected with the level of structuredness of the desired signal. This theoretic analysis aims to fill the gap between existing practical compressive imaging systems and the traditional compressive sensing theory based on random dense sensing matrices.