We present a high-accuracy, low false-alarm rate, and low computational-cost methodology for removing stars and noise and detecting space debris with low signal-to-noise ratio (SNR) in optical image sequences. First, time-index filtering and bright star intensity enhancement are implemented to remove stars and noise effectively. Then, a multistage quasi-hypothesis-testing method is proposed to detect the pieces of space debris with continuous and discontinuous trajectories. For this purpose, a time-index image is defined and generated. Experimental results show that the proposed method can detect space debris effectively without any false alarms. When the SNR is higher than or equal to 1.5, the detection probability can reach 100%, and when the SNR is as low as 1.3, 1.2, and 1, it can still achieve 99%, 97%, and 85% detection probabilities, respectively. Additionally, two large sets of image sequences are tested to show that the proposed method performs stably and effectively.