## 1 Introduction  
Gravity and gravity gradient data, essential tools in geophysical research, play a critical role in resource exploration, geological structure analysis, and navigation applications. In resource exploration, gravity data can detect subsurface density anomalies, enabling the identification of ore bodies or oil and gas reservoirs [1, 2]. For studies on geological structures, gravity data are used to analyze the density distribution of the crust and mantle and to investigate tectonic features [3, 4, 5, 6]. Gravity and gravity gradient data have also been widely employed in aided navigation, where their deep integration with multi-source sensor information significantly enhances the overall navigation accuracy and robustness in complex environments [7, 8, 9]. Gravity gradient data provide much higher spatial resolution and can detect geological anomalies at smaller scales, making them more suitable for detailed investigation of shallow geological structures [10; 11]. In practical applications, gravity gradient data also demonstrate substantial value, frequently being utilized in tasks such as edge detection [12] and depth estimation [13]. However, gravity and gravity gradient measurements often contain noise due to environmental conditions, instrumental errors, and human factors. This noise not only degrades the spatial resolution of gravity data but also reduces their ability to characterize the location and morphology of geological bodies [14; 15; 16; 17; 18]. Traditional gravity data processing methods are mostly conducted in the spatial or frequency domain, such as via direct mathematical differentiation or Fourier transform, to obtain the required gradient information [19]. In traditional methods, filtering techniques based on the spatial or frequency domain are widely applied. Low-pass filtering reduces noise by suppressing high-frequency components but tends to blur the boundary details of geological bodies [20]; the moving average method reduces noise fluctuations through local smoothing, yet causes signal distortion in non-stationary noise environments [21]; wavelet transform exhibits excellent performance in noise separation due to its multi-scale decomposition capability, but its denoising effect depends on the selection of wavelet basis functions, and its adaptability to strong nonlinear noise is limited [22]. These methods mostly rely on manually designed features or fixed parameters, making it difficult to handle the strong coupling between noise and signals in complex geological scenarios [23]. With the development of machine learning, data-driven methods have gradually emerged. Early studies employed shallow models such as Support Vector Machines (SVM) to process gravity anomalies, but they were limited by feature extraction capabilities and performed poorly in high-noise scenarios [23]. Recently, deep learning methods have achieved breakthroughs by virtue of end-to-end nonlinear mapping capabilities: The convolutional encoder-decoder structure proposed by [PERSON] et al. [24] first applied deep learning to image denoising, providing new ideas for gravity data processing; [PERSON] et al. [25] realized intelligent denoising of potential field data based on RevU-Net, verifying the potential of deep learning in the geophysical field; [PERSON] et al. [24] estimated potential field derivatives through deep neural networks, improving the stability of gradient data. However, existing deep learning methods still have two limitations: first, they lack constraints on the physical properties of the gravity field, which may generate non-physical artifacts that do not conform to the Laplace equation; second, they mostly focus on single-scale feature learning, and are insufficient in capturing the multi-scale correlations of complex geological structures [26]. Deep learning methods possess powerful capabilities for adaptive learning and non-linear modeling.