Compressed Sensing in Astronomy

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Abstract
Recent advances in signal processing have focused on the use of sparse representations in various applications. A new field of interest based on sparsity has recently emerged: compressed sensing. This theory is a new sampling framework that provides an alternative to the well-known Shannon sampling theory. In this paper, we investigate how compressed sensing (CS) can provide new insights into astronomical data compression. We first give a brief overview of the compressed sensing theory which provides very simple coding process with low computational cost, thus favoring its use for real-time applications often found onboard space mission. In practical situations, owing to particular observation strategies (for instance, raster scans) astronomical data are often redundant; in that context, we point out that a CS-based compression scheme is flexible enough to account for particular observational strategies. Indeed, we show also that CS provides a new fantastic way to handle multiple observations of the same field view, allowing us to recover low level details, which is impossible with standard compression methods. This kind of CS data fusion concept could lead to an elegant and effective way to solve the problem ESA is faced with, for the transmission to the earth of the data collected by PACS, one of the instruments onboard the Herschel spacecraft which will launched in late 2008/early 2009. We show that CS enables to recover data with a spatial resolution enhanced up to 30% with similar sensitivity compared to the averaging technique proposed by ESA.
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