Distributed Acoustic Sensing (DAS) technology has been widely applied in seismic exploration due to its advantages of low cost and high accuracy. However, DAS data is contaminated by various types of noise, among which fading noise is ubiquitously distributed. To address this issue, this paper proposes a joint denoising framework that integrates fast dictionary learning with Sequential Generalized K-means (SGK) and target-oriented median filtering. This framework utilizes SGK to replace the K-Singular Value Decomposition (K-SVD) process, specifically substituting the Singular Value Decomposition (SVD) update step. Subsequently, a statistical classification scheme is employed to effectively identify fading noise atom sequences through the construction of novel statistical parameters. Finally, targeted noise suppression is achieved via median filtering using a physics-parameterized threshold selection strategy. The denoising performance of the proposed method was validated through tests on both synthetic and real field data. By enabling precise noise localization via physics-driven statistical parameters and combining efficient dictionary learning with targeted filtering, our method significantly enhances DAS data quality, offering a novel approach for seismic signal extraction in complex noise environments.