Space Situational Awareness (SSA) relies on Low Earth Orbit (LEO) satellites to capture continuous, highresolution imagery critical for identifying space threats. The vast volume of SSA images overwhelms satellite network throughput, hindering timely transmission and processing. This paper presents a reinforcement learning (RL)-driven distributed sparse coding framework that integrates novel compression algorithms with orbital RL to address these challenges. First, we introduce an Aggregated Dictionary Learning (ADL) algorithm and a Context-aware Adaptive Binary Arithmetic Coding (CABAC) algorithm, achieving a 93.78% compression ratio by exploiting the high sparsity and spatiotemporal redundancy of SSA images. Second, the proposed compression workflow is deployed across LEO satellites in a distributed manner, where both overlapping and non-overlapping regions of images are dynamically partitioned and processed in parallel to optimize resource utilization and reduce latency. An Orbital Double Deep Q-Network (DQN) framework is proposed to optimize task offloading decisions by (1) integrating orbital dynamics into the state space, and (2) adaptively partitioning images based on visible LEO resources. Evaluations demonstrate that our framework achieves 100% task completion under visibility constraints and a 51.61% reduction on CPU and RAM occupation time compared to centralized processing.