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

TL;DR

InterIR addresses the challenge of restoring images with multiple, interacting degradations by unifying an interpretable deep unfolding framework with an ISN-based restoration engine and an input-adaptive explainable convolution. By factorizing the degradation operator and solving through alternating subproblems, InterIR maintains physical interpretability at each module while enabling image-specific adaptation. Empirical results on MDIR and SDIR benchmarks show state-of-the-art performance and strong generalization, with ablations confirming the contributions of the explainable block and interpretability-driven modules. The approach offers practical implications for robust, transparent restoration in real-world, multi-degradation scenarios.

Abstract

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.

Figures (7)

• Figure 1: Mechanisms of our method.
• Figure 2: The overall architecture of the proposed InterIR consists of an initial module followed by $n$ interpretability blocks (IPBlocks). Each IPBlock contains a restoration equation solver module (RESM), a degradation matrix update module (DMUM), and a multiplier update module (MUM).
• Figure 3: The structure of explainable block (EPBlock).
• Figure 4: Qualitative results under the MDIR experimental setup. Our InterIR produces images that are visually closer to the ground truth.
• Figure 5: Qualitative results under the SDIR experimental setup. Our InterIR is able to reconstruct finer and sharper details.