Abstract
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.
Abstract (translated)
图像恢复需要同时保留精细的局部结构和保持长距离的空间一致性。虽然卷积网络在受限的感受野方面存在困难，而Transformer在全局注意力机制下会因二次复杂度问题导致效率低下，最近的状态空间模型（如Mamba）提供了一种有吸引力的线性时间替代方案来处理长期依赖关系建模。然而，简单地将Mamba扩展到2D图像揭示了两个内在不足之处。首先，将2D特征图扁平化为1D序列会破坏空间拓扑结构，导致局部失真，阻碍精确结构恢复。其次，状态空间模型中的稳定性驱动递归动力学会导致长距离衰减，在远离的空间位置上逐渐减弱信息传递并削弱全局一致性。这些影响共同限制了高保真度图像恢复中状态空间建模的有效性。 为了解决上述问题，我们提出了渐进式分割Mamba（PS-Mamba），这是一种拓扑感知的分层状态空间框架，旨在平衡局部结构保留与高效全局传播之间的关系。不同于将整个特征图依次扁平化处理，PS-Mamba采用几何一致性的分区方法，在进入状态空间处理前保持邻域完整性。渐进式分割层次结构（半、四分之一和八分之一）能够在维护线性复杂度的同时支持结构化的多尺度建模。为了对抗长距离衰减问题，我们引入了对称跨尺度快捷通道，直接在不同层级之间传递低频全局上下文信息，从而稳定大范围空间的信息流动。 广泛的实验结果显示，在超分辨率、去噪和JPEG伪像消除方面，PS-Mamba相比于最近基于Mamba的模型以及注意力机制模型均表现出一致性的改进效果，并且优势明显。
URL
https://arxiv.org/abs/2603.09171
