Magnetic Anomaly Detection Using Spatial Frequency Domain-Based Structured Low-Rank Approximation and Block Singular Value Decomposition

In magnetic anomaly detection (MAD), the magnetic anomaly signals can be easily affected by noise in a harsh test environment, resulting in a low signal-to-noise ratio (SNR). Current MAD techniques prioritize SNR over signal characteristics and edge details, resulting in distorted signals. To tackle this issue, we propose a novel MAD method that employs structured low-rank approximation and block singular value decomposition (BSVD) in the spatial frequency domain. This approach can be termed frequency-low-rank-based BSVD (FL-BSVD). First, the low-rankness structure of the magnetic anomaly signal is obtained through 2-D discrete Fourier transform (2D-DFT) and structured Hankel transformation. Then, BSVD is applied to the Hankel matrix to reduce noise while preserving more signal edge features and enhancing detection accuracy. Finally, a field experiment comparing FL-BSVD with four commonly used methods is conducted, in which SNR, structural similarity (SSIM), mean square error (mse), and figure of merit (FOM) are employed as evaluation metrics. The experimental results demonstrate that when the initial SNR is greater than −20 dB, FL-BSVD outperforms other methods by boosting the SNR by an average of 80.79%, enhancing the SSIM by a factor of 8.9, and reducing the mse by an average of 82.74%. Especially under extremely low SNR conditions, while the other four methods fail, FL-BSVD can still partially recover the signal’s main characteristics. Furthermore, under different SNR conditions, FL-BSVD consistently outperforms the other methods in terms of FOM, clearly demonstrating the superiority of the proposed approach in edge extraction. The experiment confirms that FL-BSVD can effectively recover magnetic anomaly signal features and edge information in a strong noisy environment.