填補觀測空缺：應用於宇宙微波背景溫度場與 B 模偏振訊號補全的多尺度卷積神經網路

Abstract

在宇宙微波背景（Cosmic Microwave Background, CMB）資料分析中，取得全天空資料具有相當挑戰性，因為部分前景污染無法被有效移除。因此，典型的後續分析通常需要使用遮罩，以去除因污染而可信度較低的像素。相較於直接處理經遮罩處理後的天空資料，另一種替代方法是依據一組規則填補被遮罩的區域，此方法稱為補全（inpainting）。 本論文探討一種用於宇宙微波背景補全的多尺度卷積框架，稱為 SkyReconNet。在此框架中，我們訓練卷積神經網路（Convolutional Neural Network, CNN）來重建 CMB 圖中被遮罩而缺失的區域，同時維持資料的結構完整性。首先，我們將介紹此框架所需的 CMB 相關背景知識，接著介紹相關的機器學習概念。隨後，我們將討論目前用於 CMB 補全的方法。之後，我們將討論 SkyReconNet 的第一項應用，即 CMB 溫度圖的重建。 我們顯示，SkyReconNet 能夠重建經遮罩處理的溫度圖，其殘差大多侷限於缺失區域內，且在補全後的圖中未出現明顯的相干偽影。在球諧空間層次上，重建後的功率譜能夠在具代表性的案例中追蹤目標功率譜，並且在大部分所繪製的多極矩範圍內，與目標功率譜的差異維持在約 15% 以內。測試集平均與協方差診斷顯示其與目標模擬有整體一致性。進一步的誤差分析顯示，這種一致性本身並不足以證明其重建誤差行為已被校準。對於所測試的銀河平面遮罩，此確定性重建能保留部分類似 CMB 的球諧結構，但在遮罩像素與球諧空間診斷中皆呈現變異被抑制的情況。 接著，我們將 SkyReconNet 擴展至 CMB 偏振圖的重建。我們顯示，重建後的偏振圖能夠保留宇宙學資訊，使經校準後復原的 B 模功率譜相較於偽 spectrum 方法更能貼近目標功率譜。重建後的功率譜亦能支援穩健的宇宙學參數估計；在低至 r ~ 10^(-3) 的情況下，所有復原出的參數皆維持在 68% 可信區間內。最後，我們討論此方法未來的若干改進方向與可能延伸，包括其於實際實驗流程中的應用、不確定性估計，以及大尺度精煉。

In Cosmic Microwave Background (CMB) data analyses, obtaining full-sky data is challenging, as some foreground contamination cannot be effectively removed. Therefore, typical downstream analyses require masking to remove pixels with low confidence scores due to contamination. An alternative approach, rather than directly working with masked sky data, is to fill the masked regions according to a set of rules. This approach is called inpainting. In this thesis, we explore a multiscale convolutional framework for CMB inpainting called SkyReconNet, in which we train a Convolutional Neural Network (CNN) to reconstruct the missing regions of masked CMB maps while still maintaining the structural integrity of the data. First, we will cover the necessary CMB background required for the framework, followed by an introduction to the relevant machine-learning concepts. We will then discuss the current methodologies used for CMB inpainting. Afterward, we will discuss our first application of SkyReconNet, namely, the reconstruction of CMB temperature maps. We show that SkyReconNet reconstructs masked temperature maps with residuals largely confined to the missing regions and without obvious coherent artifacts in the completed maps. At the harmonic level, the reconstructed spectra track the target spectra in representative cases, remaining within approximately 15% over most of the plotted multipole range. Test-set averages and covariance diagnostics show broad agreement with the target simulations. A dedicated error analysis then shows that this agreement does not by itself establish calibrated reconstruction-error behavior. For the tested Galactic-plane mask, the deterministic reconstructions preserve some CMB-like harmonic structure but show variance suppression in both masked-pixel and harmonic-space diagnostics. Following that, we extend SkyReconNet to reconstruct CMB polarization maps. We show that the reconstructed polarization maps preserve cosmological information, enabling calibrated recovery of the B-mode spectrum that more closely tracks the target spectrum than the pseudo-spectrum approaches. The reconstructed spectra also support robust cosmological parameter estimation, with all recovered parameters remaining within the 68% credible interval down to r ~ 10^(-3). Lastly, we discuss several future improvements and possible extensions of this methodology, including realistic applications to experiment pipelines, uncertainty estimation, and large-scale refinement.