Computed Tomography (CT) is a vital diagnostic tool in clinical practice, yet the health risks associated with ionizing radiation cannot be overlooked. Low-dose CT (LDCT) helps mitigate radiation exposure but simultaneously leads to reduced image quality. Consequently, researchers have sought to reconstruct clear images from LDCT scans using artificial intelligence-based image enhancement techniques. However, these studies typically rely on synthetic LDCT images for algorithm training, which introduces significant domain-shift issues and limits the practical effectiveness of these algorithms in real-world scenarios. To address this challenge, we constructed a real-world paired lung dataset, referred to as Patient-uLDCT (ultra-low-dose CT), by performing multiple scans on volunteers. The radiation dose for the low-dose images in this dataset is only 2% of the normal dose, substantially lower than the conventional 25% low-dose and 10% ultra-low-dose levels. Furthermore, to resolve the anatomical misalignment between normal-dose and uLDCT images caused by respiratory motion during acquisition, we propose a novel purification strategy to construct corresponding aligned image pairs. Finally, we introduce a Frequency-domain Flow Matching model (FFM) that achieves excellent image reconstruction performance. Code is available at https://github.com/MonkeyDadLufy/flow-matching.