Precision of proportion estimation with binary compressed Raman spectrum

Abstract : The precision of proportion estimation with binary filtering of a Raman spectrum mixture is analyzed when the number of binary filters is equal to the number of present species and when the measurements are corrupted with Poisson photon noise. It is shown that the Cramer–Rao bound provides a useful methodology to analyze the performance of such an approach, in particular when the binary filters are orthogonal. It is demonstrated that a simple linear mean square error estimation method is efficient (i.e., has a variance equal to the Cramer–Rao bound). Evolutions of the Cramer–Rao bound are analyzed when the measuring times are optimized or when the considered proportion for binary filter synthesis is not optimized. Two strategies for the appropriate choice of this considered proportion are also analyzed for the binary filter synthesis.
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Philippe Réfrégier, Camille Scotté, Hilton de Aguiar, Herve Rigneault, Frédéric Galland. Precision of proportion estimation with binary compressed Raman spectrum. Journal of the Optical Society of America. A Optics, Image Science, and Vision, Optical Society of America, 2018, 35 (1), ⟨10.1364/JOSAA.35.000125⟩. ⟨hal-01715283⟩

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