Réfrégier Philippe, Scotté Camille, de Aguiar Hilton B, Rigneault Hervé, Galland Frédéric
J Opt Soc Am A Opt Image Sci Vis. 2018 Jan 1;35(1):125-134. doi: 10.1364/JOSAA.35.000125.
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.
当二元滤波器的数量等于存在物种的数量且测量受到泊松光子噪声干扰时，分析了拉曼光谱混合物二元滤波比例估计的精度。结果表明，克拉美罗界为分析这种方法的性能提供了一种有用的方法，特别是当二元滤波器正交时。证明了一种简单的线性均方误差估计方法是有效的（即方差等于克拉美罗界）。当测量时间优化或二元滤波器合成所考虑的比例未优化时，分析了克拉美罗界的变化。还分析了二元滤波器合成中适当选择该考虑比例的两种策略。
