The Internal Linear Combination (ILC) method is commonly employed to extract the cosmic microwave background (CMB) signal from multi-frequency observation maps. However, the performance of the ILC method tends to degrade when the signal-to-noise ratio (SNR) is relatively low, particularly when measuring the primordial B-modes to detect the primordial gravitational waves. To address this issue, an enhanced version of the ILC method, known as constrained ILC, is proposed. This method is designed to be more suitable for situations with low signal-to-noise ratio (SNR) by incorporating additional prior foreground information. In our study, we have modified the constraint Needlet ILC method and successfully improved its performance at low SNR. We illustrate our methods using mock data generated from the combination of WMAP, Planck and a ground-based experiment in the northern hemisphere, and the chosen noise level for the ground-based experiment are very conservative which can be easily achieved in the very near future. The results show that the level of foreground residual can be well controlled. In comparison to the standard NILC method, which introduces a bias to the tensor-to-scalar ratio (r) of approximately 0.05, the constrained NILC method exhibits a significantly reduced bias of only around 5 × 10^-3 towards r which is much smaller than the statistical error.

中文翻译：

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CMB B 模式观测的约束 NILC 方法

内部线性组合（ILC）方法通常用于从多频观测图中提取宇宙微波背景（CMB）信号。然而，当信噪比 (SNR) 相对较低时，特别是在测量原始信号时，ILC 方法的性能往往会下降。乙- 探测原始引力波的模式。为了解决这个问题，提出了 ILC 方法的增强版本，称为约束 ILC。该方法通过结合额外的先验前景信息而设计，更适合低信噪比（SNR）的情况。在我们的研究中，我们修改了约束Needlet ILC方法并成功提高了其在低SNR下的性能。我们使用 WMAP、普朗克和北半球地面实验相结合生成的模拟数据来说明我们的方法，并且地面实验所选择的噪声水平非常保守，可以在不久的将来轻松实现。结果表明，前景残差水平可以得到很好的控制。与标准 NILC 方法相比，该方法引入了张量与标量比的偏差 (r）约为 0.05，约束 NILC 方法表现出显着降低的偏差，仅约 5 × 10 ^-3r这比统计误差要小得多。