# Physically Interpretable Multi-Degradation Image Restoration via Deep Unfolding and Explainable Convolution

arXiv: https://arxiv.org/abs/2511.10166 · HTML: https://mlsanity.com/paper/2511.10166/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 56 references that are in the map.
- First posted on arXiv 13 Nov 2025.

## Builds on (most cited first, 30 of 30)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Multi-Stage Progressive Image Restoration](https://mlsanity.com/paper/2102.02808/) (2021)
- [Simple Baselines for Image Restoration](https://mlsanity.com/paper/2204.04676/) (2022)
- [Benchmarking Single Image Dehazing and Beyond](https://mlsanity.com/paper/1712.04143/) (2017)
- [Deep Joint Rain Detection and Removal from a Single Image](https://mlsanity.com/paper/1609.07769/) (2016)
- [MambaIR: A Simple Baseline for Image Restoration with State-Space Model](https://mlsanity.com/paper/2402.15648/) (2024)
- [Multi-Scale Progressive Fusion Network for Single Image Deraining](https://mlsanity.com/paper/2003.10985/) (2020)
- [Density-aware Single Image De-raining using a Multi-stream Dense Network](https://mlsanity.com/paper/1802.07412/) (2018)
- [Image De-raining Using a Conditional Generative Adversarial Network](https://mlsanity.com/paper/1701.05957/) (2017)
- [PromptIR: Prompting for All-in-One Blind Image Restoration](https://mlsanity.com/paper/2306.13090/) (2023)
- [AdaIR: Adaptive All-in-One Image Restoration via Frequency Mining and Modulation](https://mlsanity.com/paper/2403.14614/) (2024)
- [MambaIRv2: Attentive State Space Restoration](https://mlsanity.com/paper/2411.15269/) (2024)
- [DEA-Net: Single image dehazing based on detail-enhanced convolution and content-guided attention](https://mlsanity.com/paper/2301.04805/) (2023)
- [Perceive-IR: Learning to Perceive Degradation Better for All-in-One Image Restoration](https://mlsanity.com/paper/2408.15994/) (2024)
- [Vision-Language Gradient Descent-driven All-in-One Deep Unfolding Networks](https://mlsanity.com/paper/2503.16930/) (2025)
- [Visual-Instructed Degradation Diffusion for All-in-One Image Restoration](https://mlsanity.com/paper/2506.16960/) (2025)
- [AdaRevD: Adaptive Patch Exiting Reversible Decoder Pushes the Limit of Image Deblurring](https://mlsanity.com/paper/2406.09135/) (2024)
- [Prompt-based Ingredient-Oriented All-in-One Image Restoration](https://mlsanity.com/paper/2309.03063/) (2023)
- [LoFormer: Local Frequency Transformer for Image Deblurring](https://mlsanity.com/paper/2407.16993/) (2024)
- [Attention-based Adaptive Selection of Operations for Image Restoration in the Presence of Unknown Combined Distortions](https://mlsanity.com/paper/1812.00733/) (2018)
- [Rotation Equivariant Proximal Operator for Deep Unfolding Methods in Image Restoration](https://mlsanity.com/paper/2312.15701/) (2023)
- [Mixed Hierarchy Network for Image Restoration](https://mlsanity.com/paper/2302.09554/) (2023)
- [Prior-guided Hierarchical Harmonization Network for Efficient Image Dehazing](https://mlsanity.com/paper/2503.01136/) (2025)
- [Adaptive Rectangular Convolution for Remote Sensing Pansharpening](https://mlsanity.com/paper/2503.00467/) (2025)
- [Intra and Inter Parser-Prompted Transformers for Effective Image Restoration](https://mlsanity.com/paper/2503.14037/) (2025)
- [Restoring Spatially-Heterogeneous Distortions using Mixture of Experts Network](https://mlsanity.com/paper/2009.14563/) (2020)
- [DIVA: Deep Unfolded Network from Quantum Interactive Patches for Image Restoration](https://mlsanity.com/paper/2301.00247/) (2022)
- [Joint Edge Optimization Deep Unfolding Network for Accelerated MRI Reconstruction](https://mlsanity.com/paper/2405.05564/) (2024)

## Abstract (arXiv)

Although image restoration has advanced significantly, most existing methods target only a single type of degradation. In real-world scenarios, images often contain multiple degradations simultaneously, such as rain, noise, and haze, requiring models capable of handling diverse degradation types. Moreover, methods that improve performance through module stacking often suffer from limited interpretability. In this paper, we propose a novel interpretability-driven approach for multi-degradation image restoration, built upon a deep unfolding network that maps the iterative process of a mathematical optimization algorithm into a learnable network structure. Specifically, we employ an improved second-order semi-smooth Newton algorithm to ensure that each module maintains clear physical interpretability. To further enhance interpretability and adaptability, we design an explainable convolution module inspired by the human brain's flexible information processing and the intrinsic characteristics of images, allowing the network to flexibly leverage learned knowledge and autonomously adjust parameters for different input. The resulting tightly integrated architecture, named InterIR, demonstrates excellent performance in multi-degradation restoration while remaining highly competitive on single-degradation tasks.