Sleep plays a pivotal role in the quality of life, and sleep posture is related to many medical conditions such as sleep apnea. In this paper, we design a dense pressure-sensitive bedsheet for sleep posture monitoring. In contrast to existing techniques, our bedsheet system offers a completely unobtrusive method using comfortable textile sensors. Based on high-resolution pressure distributions from the bedsheet, we develop a novel framework for pressure image analysis to monitor sleep postures, including a set of geometrical features for sleep posture characterization and three sparse classifiers for posture recognition. We run a pilot study and evaluate the performance of our methods with 14 subjects to analyze 6 common postures. The experimental results show that our proposed method enables reliable sleep posture recognition and offers better overall performance than state-of-the-art methods, achieving up to 83.0% precision and 83.2% recall on average.