Hankel Tensor Correlation Analysis Coupled With Total Variation Regularization for Sparse Data Reconstruction in Magnetic Field Sensing Systems

As crucial spatio-temporal observation data, the geomagnetic field exhibits significant application value for earthquake precursor monitoring and space weather forecasting. However, practical geomagnetic observations are frequently compromised by random missing points and fiber missing patterns due to instrument malfunctions and electromagnetic interference, substantially limiting data reliability for operational applications. Although current reconstruction approaches predominantly rely on tensor decomposition theory, conventional techniques do not adequately capture the intrinsic structural characteristics of geomagnetic data. In particular, in complex missing scenarios, these methods demonstrate limited reconstruction accuracy due to ineffective data recovery. To address these limitations, the study propose a novel sparse geomagnetic data reconstruction method incorporating spatio-temporal Hankel tensor correlation and total variation (HKTCTV). The methodology involves: 1) organizing geomagnetic data into a third-order tensor spanning sampling intervals, days, and locations; 2) applying Hankel transformation to exploit low-rank properties; 3) employing tensor-correlated total variation to characterize local smoothness priors. The resulting tensor model is solved via the alternating-direction multiplier method. Experimental validation using real geomagnetic station data demonstrates that HKTCTV achieves average accuracy improvements of 40% for random missing scenarios and 80% for mixed random-fiber missing cases compared to state-of-the-art methods (OTNN, FCTN-FR, OTSVD), confirming the method’s superior performance.