# Physics-Based Noise Modeling and Deep Learning for Denoising Permanently Shadowed Lunar Images
## 1 Introduction  
The Moon, as a core target for human deep-space exploration, holds irreplaceable value in scientific research, resource exploration, and mission planning through its high-resolution surface images. These images can accurately reveal the Moon's topographic and geological features, providing critical data to study its evolutionary history, crustal composition, and resource distribution, while also laying the foundation for the safe landing and execution of future missions. Currently, high-resolution images captured by the Lunar Reconnaissance Orbiter Camera (LROC) Narrow-Angle Cameras (NACs) have become a vital data source for lunar research, offering important insights for topographic analysis, geological composition studies, and geomorphic process exploration, significantly advancing the study of the Moon's formation history, resource assessment, and precision landing missions [1, 2]. Moreover, the permanently shadowed regions (PSRs) of the Moon, due to their unique polar lighting conditions, have garnered significant attention. Due to the Moon's small axial tilt and low solar elevation angle, deep craters in the polar regions receive no direct sunlight year-round. They primarily rely on weak scattered light from nearby terrain and starlight, resulting in a very limited number of photonsdetected by cameras. Consequently, photon noise and sensor noise dominate the LROC NAC images [3; 4], obscuring key topographic information and urgently requiring effective denoising techniques to improve image quality. Enhancing the clarity of PSR images is crucial for advancing lunar exploration. In the field of traditional image denoising, several classic methods have been proposed, which are generally categorized into three main types: filtering methods, variational methods, and statistical modeling methods [5; 6; 7; 8; 9]. Among the filtering methods, the non-local means filter, introduced by [PERSON] et al. (2005), utilizes the self-similarity of images by calculating similarity weights between pixel blocks and performing weighted averaging to achieve denoising. This method is effective in preserving image details and textures [10]. In the realm of variational methods, the total variation denoising model proposed by [PERSON] et al. (1992) removes noise by minimizing the total variation of the image. This model assumes that natural images exhibit piecewise smooth characteristics, allowing it to smooth noise in homogeneous regions while preserving edge information. It is particularly suitable for images with prominent edge structures [11]. In the domain of statistical modeling methods, [PERSON] et al. (2003) introduced the Gaussian scale mixture model for wavelet-domain denoising. By applying wavelet transforms to decompose the image and statistically modeling the wavelet coefficients, they assumed the coefficients followed a Gaussian scale mixture distribution and optimized them through Bayesian estimation. This significantly enhanced denoising performance, especially in terms of preserving image details and textures [12]. Additionally, [PERSON] et al. (2007) proposed the block-matching and 3D transform-domain filtering method, which groups similar image blocks and performs collaborative filtering in the transform domain. This method leverages the sparsity of the transform coefficients to remove noise, making it particularly effective for Gaussian noise removal [13]. These traditional denoising methods have demonstrated excellent performance across various noise models and are capable of effectively preserving both image details and structure. With the development of deep learning technologies, more and more research have adopted deep learning methods to tackle denoising problems, which typically perform well under various noise conditions [14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28]. Convolutional Neural Networks are the most commonly used denoising models. Among these, [PERSON] et al.