线性化迭代最小二乘法（LIL）：用于多频CMB实验（如普朗克实验）中成分分离的参数拟合算法
Linearized iterative least-squares (LIL): A parameter fitting algorithm for component separation in multifrequency CMB experiments such as Planck
摘要：
我们提出了一个有效的算法，最小二乘参数拟合优化的多频CMB实验中的成分分离。我们避开了一些与非线性优化相关的问题，利用准线性性质的前景模型。我们在公开的普朗克天空模型FFP 6模拟上演示了我们的算法，线性化迭代最小二乘（LIL），并将我们的结果与其他算法进行了比较。我们的工作在全普朗克分辨率，并表明，降低所有通道的分辨率的最低频率通道是没有必要的。最后，我们提出了公开可用的普朗克数据的结果。我们的算法非常快，在不到160 CPU分钟（或在几十个核心上并行运行几分钟）的时间内以全分辨率（5000万像素）将6个参数拟合到7个最低的普朗克通道。因此，LIL很容易扩展到未来的实验，可能有更高的分辨率和更多的频率通道。我们还自然地传播不同参数的不确定性，由于在地图中的噪声以及退化的参数之间的最终误差的参数使用Fisher矩阵。LIL的一个间接应用可以是贝叶斯参数拟合的前端，以找到最大的可能性，作为吉布斯抽样的起点。我们表明，对于罕见的成分，如一氧化碳排放，目前在天空中的一小部分，最佳的方法应该结合参数拟合模型选择。LIL在满足准线性标准的其他天体物理应用中也是有用的。
英文摘要：
We present an efficient algorithm for the least squares parameter fitting optimized for component separation in multi-frequency CMB experiments. We sidestep some of the problems associated with non-linear optimization by taking advantage of the quasi-linear nature of the foreground model. We demonstrate our algorithm, linearized iterative least-squares (LIL), on the publicly available Planck sky model FFP6 simulations and compare our result with the other algorithms. We work at full Planck resolution and show that degrading the resolution of all channels to that of the lowest frequency channel is not necessary. Finally we present results for the publicly available Planck data. Our algorithm is extremely fast, fitting 6 parameters to 7 lowest Planck channels at full resolution (50 million pixels) in less than 160 CPU-minutes (or few minutes running in parallel on few tens of cores). LIL is therefore easily scalable to future experiments which may have even higher resolution and more frequency channels. We also naturally propagate the uncertainties in different parameters due to noise in the maps as well as degeneracies between the parameters to the final errors on the parameters using Fisher matrix. One indirect application of LIL could be a front-end for Bayesian parameter fitting to find the maximum of the likelihood to be used as the starting point for the Gibbs sampling. We show for rare components, such as the carbon-monoxide emission, present in small fraction of sky, the optimal approach should combine parameter fitting with model selection. LIL may also be useful in other astrophysical applications which satisfy the quasi-linearity criteria.
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