Image restoration requires simultaneously preserving fine-grained local structures and maintaining long-range spatial coherence. While convolutional networks struggle with limited receptive fields, and Transformers incur quadratic complexity for global attention, recent State Space Models (SSMs), such as Mamba, provide an appealing linear-time alternative for long-range dependency modelling. However, naively extending Mamba to 2D images exposes two intrinsic shortcomings. First, flattening 2D feature maps into 1D sequences disrupts spatial topology, leading to locality distortion that hampers precise structural recovery. Second, the stability-driven recurrent dynamics of SSMs induce long-range decay, progressively attenuating information across distant spatial positions and weakening global consistency. Together, these effects limit the effectiveness of state-space modelling in high-fidelity restoration. We propose Progressive Split-Mamba (PS-Mamba), a topology-aware hierarchical state-space framework designed to reconcile locality preservation with efficient global propagation. Instead of sequentially flattening entire feature maps, PS-Mamba performs geometry-consistent partitioning, maintaining neighbourhood integrity prior to state-space processing. A progressive split hierarchy (halves, quadrants, octants) enables structured multi-scale modelling while retaining linear complexity. To counteract long-range decay, we introduce symmetric cross-scale shortcut pathways that directly transmit low-frequency global context across hierarchical levels, stabilising information flow over large spatial extents. Extensive experiments on super-resolution, denoising, and JPEG artifact reduction show consistent improvements over recent Mamba-based and attention-based models with a clear margin.