Progressive Split Mamba: Effective State Space Modelling for Image Restoration

Image restoration aims to recover high-quality images from degraded observations. Recent Mamba-based image restoration models have demonstrated strong potential in modeling long-range dependencies with linear complexity. However, most existing designs still rely on a single state-evolution timescale, which limits their adaptability to spatially heterogeneous and task-dependent degradation patterns in all-in-one image restoration. In this paper, we propose Multi-$τ$ Liquid-Mamba, an adaptive state space module that introduces input-conditioned multi-timescale liquid discretization into selective state space modeling. Instead of changing the overall selective scan pipeline, the proposed module modulates the effective discretization steps of multiple dynamical branches and adaptively fuses their responses according to degradation-aware gating weights. This design allows the model to capture both fast-varying local details and slowly evolving global structures while preserving the linear scaling property of Mamba with respect to sequence length. Importantly, Multi-$τ$ Liquid-Mamba modulates the effective transition dynamics while preserving the original selective parameterization and hardware-efficient selective scan mechanism, making it a plug-and-play module that can be seamlessly integrated into existing Mamba-based architectures. Built upon this framework, we develop a Multi-$τ$ Liquid-Mamba Image Restoration Network (MLMIR) for all-in-one image restoration. Extensive experiments on a wide range of restoration benchmarks demonstrate that MLMIR consistently achieves state-of-the-art performance in all-in-one image restoration while remaining highly competitive in task-aligned restoration settings.

State space models (SSMs) have emerged as a powerful paradigm for efficient single-image super-resolution (SR) due to their linear complexity and long-range modeling capabilities. However, existing Mamba-based methods typically rely on data-agnostic rigid scanning, which reshapes 2D images into 1D sequences over a fixed grid, inevitably disrupting spatial-semantic topology and introducing artifacts. Inspired by the Gestalt perceptual grouping theory, we propose SP-MoMamba, a superpixel-driven mixture of state space experts designed for content-aware SR. Our core idea is to transform the traditional rigid scanning into a semantic-level interaction by treating superpixels as fundamental units. Specifically, we introduce the Superpixel-driven State Space Model (SP-SSM), which compresses semantically homogeneous regions into high-order tokens to preserve global topological consistency. To address the conflict between fixed scanning scales and diverse semantic granularities, we develop the Multi-Scale Superpixel Mixture of State Space Experts (MSS-MoE). This module utilizes a dynamic routing mechanism to adaptively assign scale-specific experts, effectively capturing multi-scale textures while reducing computational redundancy. Furthermore, to prevent the loss of high-frequency details during global abstraction, we introduce a Local Spatial Modulation Expert (LSME) to complement the global modeling, ensuring a precise reconstruction of sharp edges and fine structures. Extensive experiments on standard benchmarks demonstrate that SP-MoMamba achieves superior reconstruction fidelity and a more favorable efficiency-performance trade-off compared to state-of-the-art efficient SR methods.

Old photographs often suffer from multiple coupled degradations, including scratches, cracks, fading, blur, noise, and missing regions, severely degrading both visual quality and semantic content. We propose Loop-Mamba, a lightweight loop-based state-space framework that formulates old photo restoration as progressive state evolution, where a persis- tent restoration state is continuously propagated and refined through iterative computation. Specifically, we introduce a Semantic-Guided Degradation Estimator (SGDE) to explicitly model heterogeneous degradations by jointly predicting local degradation maps and global degradation scores, providing degradation-aware guidance for state evolution. We further develop a Shared Structural Memory Mamba (S$^2$M- Mamba), which maintains a persistent restoration state across iterations, enabling persistent state evolution through shared structural memory for robust long-range structural reconstruction. Benefiting from first-order state recursion, Loop-Mamba propagates latent restoration states through recurrent tran- sitions instead of repeatedly stacking deep feature transformations, thereby alleviating gradient dilution while avoiding the computational overhead inherent in iterative CNN- and Transformer-based restoration frameworks. A lightweight multi-directional scanning strategy further enhances direc- tional information aggregation and preserves structural continuity. To better evaluate restoration quality, we introduce the task-oriented Old Photo Damage Recovery Score (ODRS), which jointly measures degradation recovery and structural reconstruction fidelity. Experimental results on the public SynOld benchmark demonstrate that Loop-Mamba consistently outperforms previous state-of-the-art methods across both conventional restoration metrics and the proposed ODRS.