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The authors propose an analysis of some connections existing between sparse estimation and detection tests. In addition to the Generalized Likelihood Ratio (GLR) and to the Bayes Factor, they consider two tests based on Maximum A Posteriori estimates of the sparse vector parameter. These detection tests are then set in order to take advantage of a redundant dictionary, and to account for instrument and noise characteristics specific to the MUSE integral field spectrograph, which will deliver astrophysical hyper spectral data. They use in this framework a specific representation dictionary, designed by finely discretising elementary spectral features (lines with various widths, steps, and continuum parameterization). They show that the proposed detection strategy is efficient, and outperforms the GLR.
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