As the number of low Earth orbit satellites is increasing, new algorithms and high-performance computing resources are needed to handle the enormous real-time arrival data generated by satellites. Based on the requirements, this paper proposes a novel real-time adaptive speckle filtering selection algorithm for satellite synthetic aperture radar (SAR) images. The use of high-performance filters generates high-quality images whereas it introduces delays. Thus, a real-time adaptive algorithm which achieves time-average SAR image quality maximization subject to delays using Lyapunov optimization, where the delay is formulated with a queuing model. Evaluation results show that the proposed algorithm guarantees desired performance improvements.