Sparse Geomagnetic Time-Series Sensing Data Completion Leveraging Improved Tensor Correlated Total Variation

Geomagnetic field data, a form of spatiotemporal data, holds significant importance in predicting earthquakes and magnetic storms. However, challenges arise due to missing data caused by factors like hardware failures and environmental interferences, hindering further research. In recent years, tensor-based data completion methods have garnered attention due to their ability to capture the inherent nonlinear relationships within data. Driven by the observed high correlation and consistent overall trends in geomagnetic data across different regions, this research endeavors to harness the inherent low-rank and smoothing properties of such data. An innovative approach is introduced, which combines a smoothing prior with a low-rank prior, resulting in the development of an improved tensor correlated total variation (ITCTV)-based method for completing sparse geomagnetic data. Initially, the low-rank and smooth characteristics of geomagnetic data are validated, and sparse geomagnetic tensors are constructed as model inputs, accommodating both fiber and random missing data scenarios. Subsequently, an advanced tensor-related total variation (TV) norm is devised to concurrently capture the low-rank and smooth prior information of the sparse geomagnetic data. An optimized alternating direction multiplier method is then implemented to solve the tensor completion model. Evaluations conducted using synthetic datasets from 13 actual geomagnetic stations reveal that leveraging the physical attributes of geomagnetic data as prior information for analysis significantly enhances data completion, mitigates noise interference, and boosts the accuracy and credibility of earthquake and magnetic storm predictions. Compared to conventional tensor completion techniques like BGCP, FCTN, and PSTNN, the proposed method achieves an average improvement of roughly 20% in completion accuracy for random missing scenarios, and an exceptional improvement exceeding 90% in scenarios involving both random and fiber missing data.