Processing and compression of noise-dominated data: application to the cosmic microwave background data on board the Planck satellite |
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| Authors: | E Gaztañaga A Romeo J Barriga E Elizalde |
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| Institution: | INAOE, Astrofisica, Tonantzintla, Apdo Postal 216 y 51, 7200 Puebla, Mexico;Institut d'Estudis Espacials de Catalunya (IEEC/CSIC), Institut de Ciències de l'Espai (CSIC), Edifici Nexus-201 –c/ Gran Capità2-4, 08034 Barcelona, Spain |
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| Abstract: | We address the problem of encoding and compressing data dominated by noise. Information is decomposed into 'reference' sequences plus arrays containing noisy differences susceptible to being described by a known probability distribution. One can then give reliable estimates of the optimal compression rates by estimating the corresponding Shannon entropy. As a working example, this idea is applied to an idealized model of the cosmic microwave background (CMB) data on board the Planck satellite. Data reduction is a critical issue in space missions because the total information that can be downloaded to Earth is sometimes limited by telemetry allocation. Similar limitations might arise in remotely operated ground based telescopes. This download-rate limitation could reduce the amount of diagnostics sent on the stability of the instruments and, as a consequence, curb the final sensitivity of the scientific signal. Our proposal for Planck consists of taking differences of consecutive circles at a given sky pointing. To a good approximation, these differences could be made independent of the external signal, so that they are dominated by thermal (white) instrumental noise, which is simpler to model than the sky signal. Similar approaches can be found in other individual applications. Generic simulations and analytical predictions show that high compression rates,  can be obtained with minor or zero loss of sensitivity. Possible effects of digital distortion are also analysed. The proposed scheme is flexible and reliable enough to be optimized in relation to other critical aspects of the corresponding application. For Planck , this study constitutes an important step towards a more realistic modelling of the final sensitivity of the CMB temperature anisotropy maps. |
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| Keywords: | methods: data analysis methods: statistical techniques: miscellaneous cosmic microwave background cosmology: observations |
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