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

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.