Reconstruction of sparse magnetic anomaly data by integrating spatially adaptive mean compensation with patch-based sparse coding

Abstract High-precision geomagnetic data is crucial for resource exploration and navigation. This paper proposes a reconstruction method integrating spatially adaptive mean compensation with patch-based sparse coding (MC-SC), which features a resolution-self-adaptive joint dictionary training strategy and a spatially adaptive MC module to preserve low-frequency backgrounds and recover high-frequency details. Experiments on three aeromagnetic survey regions show that MC-SC outperforms existing methods iterative back projection convolutional neural network (IBP and CNN) in reconstruction accuracy and detail fidelity. At a 50 m grid scale, MC-SC achieves a peak signal-to-noise ratio of 55.57 dB in Herat, significantly higher than IBP (52.89 dB) and CNN (52.64 dB). Moreover, under noisy conditions (up to 10 nT Gaussian noise), MC-SC exhibits superior robustness with slower performance degradation and more concentrated error distributions. The method provides a reliable solution for high-resolution geomagnetic data reconstruction from sparse samples, with strong potential for navigation and mapping applications.