# Physics-Based Noise Modeling and Deep Learning for Denoising Permanently Shadowed Lunar Images
## 1 Introduction
(2021) first proposed a random neighbor sub-sampler to generate training image pairs, then trained a denoising network on the subsampled training pairs from the first stage and introduced an additional loss function for better performance. This method eliminates the need for noise-clean image pairs, multiple noise observations, or explicit noise modeling [14]. [PERSON] et al. (2020) designed a non-local subspace attention module for learning basis generation and subspace projection, training a network that separates signal and noise by learning a set of reconstruction bases in the feature space. This method successfully recovers high-quality images in scenes with weak textures or high-frequency details [15]. [PERSON] et al. (2021) proposed a lightweight neural network solution to handle complex noise in real images, such as shot noise and companding noise. The network is reversible and suitable for denoising tasks, improving performance through deep supervised learning. Its lightweight design makes it applicable to embedded systems and mobile devices while achieving efficient denoising without losing original image information [16]. [PERSON] et al. (2021) focused on addressing Poisson-Gaussian mixed noise, proposing a fast blind denoiser that effectively removes mixed noise from images without prior knowledge of the noise level [17]. In summary, traditional denoising strategies are computationally efficient and perform well under relatively simple conditions but often struggle with more complex noise distributions. On the other hand, deep learning-based methods, although often requiring more computational resources, exhibit strong capabilities in extracting significant featuresand handling complex noise types [21]. Given these advantages, data-intensive projects increasingly prefer deep learning methods in scenarios requiring higher-quality outputs, especially when ample data and computational power are available. Although significant progress has been made in image denoising, existing research primarily focuses on Earth images, with relatively little attention given to denoising lunar PSR images. Compared to Earth images, lunar PSR images have significantly reduced contrast due to limited lighting conditions, making it difficult to separate topographic features and geological structures, thus increasing the complexity of subsequent analysis. Additionally, the working conditions of the LROC NAC imaging system differ from those of Earth cameras, and the images may contain various noise components, such as Poisson noise and stripe noise, significantly increasing denoising difficulty. Furthermore, the variation in solar incident angle and the diversity of terrain lead to uneven lighting, with some areas being dim while others are relatively bright, further complicating image processing. Therefore, applying traditional models trained on Earth image denoising datasets to lunar PSR images presents challenges in effectively removing photon noise and stripe noise. This study proposes a denoising method for lunar PSR images that combines a physical noise model and deep learning techniques [29; 30; 31; 32; 33; 34]. The main contributions of this study can be summarized as follows:  
1. This study integrates the physical noise model with deep learning, simulating the noise distribution and intensity in LROC NAC lunar PSR images, enhancing the denoising capability of the model and providing a physics-based simulation method for constructing training datasets, thereby improving the physical interpretability of the network model. 2. This study proposes a full-scale feature refinement and local enhancement shifted window multi-head self-attention Transformer (FRET) network, which effectively captures multi-resolution noise and details through full-scale skip connections and enhances denoising accuracy and detail recovery using the self-attention mechanism of Transformers. 3.