Loop-Mamba: A Loop Mamba with Degradation-Aware and Shared Memory for Old Photo Restoration

The gist The proposed Loop-Mamba framework formulates old photo restoration as a progressive loop state evolution process, enabling continuous restoration through recurrent state propagation rather than repeated image reconstruction<ref:2608.02346#pg2>

Problem Formulation

Old photo restoration is formulated as a progressive state evolution process where a latent restoration state evolves under degradation-aware guidance, St+1 = F(St, Id, D)<ref:2608.02346#pg4> This contrasts with the conventional formulation where old photo restoration is treated as a direct image-to-image mapping Ir = fθ(Id)<ref:2608.02346#pg4> The goal is to recover the clean counterpart Igt after T iterations by reconstructing the image as ˆI = R(ST)<ref:2608.02346#pg2>

Semantic-Guided Degradation Representation

To model heterogeneous degradations explicitly, a Semantic-Guided Degradation Estimator (SGDE) is introduced to jointly predict a pixel-level degradation map and an image-level degradation score<ref:2608.02346#pg3> Given the degraded input image Id, the SGDE extracts degradation-aware features using a lightweight encoder, Fd = Ed(Id)<ref:2608.02346#pg4> The local degradation map Dl is predicted as Dl = σ (ϕl(Fd))<ref:2608.02346#pg5> Meanwhile, the global degradation score Dg is obtained by Dg = σ (ϕg (GAP(Fd)))<ref:2608.02346#pg6> The resulting degradation representation is defined as D = [Dl, Dg]<ref:2608.02346#pg8> This representation is subsequently used to guide degradation-aware state evolution throughout the restoration process<ref:2608.02346#pg2>

Loop State Evolution

The restoration process involves three components: degradation-modulated state update, shared structural memory evolution, and multi-directional state transition<ref:2608.02346#pg2> The degradation-guided state update is formulated as Set = St + Dl ⊙ ϕ(St) + Dg · ψ(St)<ref:2608.02346#pg9> This modulated state is then propagated through the Mamba state transition, St+1 = M(Set)<ref:2608.02346#pg10> To preserve global structural consistency, a Shared Structural Memory (S2M) continuously accumulates and propagates structural representations throughout the restoration process<ref:2608.02346#pg10> The memory is recursively updated by Mt+1 = (1 − α)Mt + αSt+1 The updated memory is subsequently fused into the current restoration state, Sbt+1 = St+1 + βMt+1

Multi-Directional State Propagation

To enhance spatial information propagation, a lightweight multidirectional scanning strategy is adopted to perform state evolution along multiple spatial directions The directional state sequences are first generated by nZ(k)o4 k=1 = T (Sbt+1) Each sequence is then propagated using the shared Mamba state evolution operator, H(k) = M(Z(k)), k = 1..., 4 Finally, the propagated states are aggregated as S∗t+1 = A(H(1), H(2), H(3), H(4)) Multidirectional propagation enriches long-range interactions with negligible computational overhead

Optimization Objective and Evaluation

Loop-Mamba is optimized using a joint reconstruction and degradation supervision objective, L = Lrec + λdLdeg The reconstruction loss is defined as Lrec = λ1LL1 + λ2LSSIM + λ3Ledge + λ4LT V The degradation supervision loss is Ldeg = (Dg − Dˆg) 2 The task-oriented evaluation metric, Old Photo Damage Recovery Score (ODRS), jointly measures degradation recovery and structural reconstruction fidelity ODRS is defined as ODRS = wdDRS + wsSRS 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<ref:2608.02346#pg2>

Conclusion

Loop-Mamba is a lightweight state-space framework for old photo restoration based on progressive state evolution<ref:2608.02346#pg2> By integrating semantic-guided degradation estimation, shared structural memory, and direction-aware multi-scan propagation, the proposed method effectively models heterogeneous degradations while progressively refining restoration states The paper concludes that Loop-Mamba achieves the best PSNR, SSIM, FSIM, and ODRS while requiring substantially fewer FLOPs and MACs and achieving the highest inference speed on 1080P images<ref:2608.02346#pg2> This demonstrates an excellent quality-efficiency tradeoff<ref:2608.02346#pg2> The visual results confirm that Loop-Mamba consistently produces cleaner structures and finer textures, while effectively suppressing various degradations such as noise, blur, and color shifts The model's feasibility is further demonstrated through its deployment on a Mi 10 Lite Zoom smartphone using ONNX Runtime This confirms its practical applicability for efficient mobile deployment The progressive state evolution of Loop-Mamba across five restoration cycles shows that the error maps become progressively smoother, indicating that residual errors are gradually eliminated

Ablation Study Insights

The ablation study on the proposed modules confirms that SGDE (V2) improves DRS and ODRS through explicit degradation modeling, while S2M (V3) and DMS (V4) enhance structural consistency and local texture reconstruction, respectively Increasing the state dimension d yields diminishing performance gains at substantially higher computational cost, indicating that a moderate state dimension is already sufficient to capture most restoration information The restoration performance first improves and then gradually declines as t increases, suggesting that early state evolution effectively accumulates restoration information while excessive iterations lead to slight over-refinement A default configuration of d = 16 is adopted for the best quality-efficiency trade-off The performance comparison on the Stockfilm real-world dataset shows that Loop-Mamba achieves the best BRISQUE score and competitive TOPIQ and MAN-IQA scores, demonstrating its effectiveness in perceptual quality enhancement This confirms its superior performance compared to other methods like MambaIRv2 on the Stockfilm dataset The model's ability to perform on-device restoration of real degraded photographs while maintaining satisfactory visual quality demonstrates its feasibility for efficient mobile deployment The paper presents a comprehensive solution that addresses the challenges of heterogeneous degradation modeling and persistent state propagation in old photo restoration through a novel loop-based state-space framework<ref:2608.02346#pg2> This work establishes a new paradigm for progressive image restoration by focusing on recurrent state evolution rather than repeated feature reconstruction<ref:2608.02346#pg2> The introduction of the task-oriented metric ODRS provides a robust way to jointly evaluate degradation recovery and structural reconstruction fidelity This framework is highly competitive against existing state-of-the-art methods across various metrics and real-world scenarios<ref:2608.

1. The Loop-Mamba framework can be used to formulate old photo restoration as a progressive loop state evolution process rather than repeated image reconstruction. This enables continuous restoration through recurrent state propagation rather than repeated image reconstruction, leading to more robust long-range structural reconstruction.

2. Integrating the Semantic-Guided Degradation Estimator (SGDE) allows for a degradation-aware state evolution where the dynamics adaptively focus on severely degraded regions by incorporating local degradation maps and global scores into the state update equation: Set = St + Dl ⊙ ϕ(St) + Dg · ψ(St).

3. The Shared Structural Memory Mamba (S2M) enables persistent structural state propagation, as it continuously accumulates and propagates structural representations throughout the restoration process, which preserves previously recovered content to avoid loss under severe degradations.

4. The multi-directional state propagation strategy enhances spatial information aggregation by generating directional state sequences and propagating them using the shared Mamba operator, thereby enriching long-range interactions with negligible computational overhead.

5. The system can be optimized using a joint objective that balances fidelity and degradation modeling: L = Lrec + λdLdeg, where Lrec ensures pixel fidelity and structural consistency, while Ldeg supervises the predicted degradation scores.

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 squared 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.