Air transport poses significant environmental challenges, particularly the contribution of flight contrails to climate change due to their potential global warming impact. Detecting contrails from satellite images has been a long-standing challenge. Traditional computer vision techniques have limitations under varying image conditions, and machine learning approaches using typical convolutional neural networks are hindered by the scarcity of hand-labeled contrail datasets and contrail-tailored learning processes. In this paper, we introduce an innovative model based on augmented transfer learning that accurately detects contrails with minimal data. We also propose a novel loss function, SR Loss, which improves contrail line detection by transforming the image space into Hough space. Our research opens new avenues for machine learning-based contrail detection in aviation research, offering solutions to the lack of large hand-labeled datasets, and significantly enhancing contrail detection models.