VMD Optimization Using a Logistic-Map-Enhanced BTO Algorithm and a Dual-Head Attention LSTM for Magnetocardiography Signals Denoising

Magnetocardiography (MCG) is highly susceptible to noise during acquisition, which significantly limits its clinical utility for the assessment of Coronary Artery Disease (CAD). Traditional model-driven and data-driven denoising methods often suffer from manual parameter tuning, inadequate feature preservation, and limited adaptability, resulting in suboptimal performance in noisy environments. To address these challenges, this paper introduces a novel hybrid model-driven and data-driven framework called LBTO-VMD-DLSTM. The framework utilizes a logistic-map-enhanced Bermuda Triangle Optimization (LBTO) algorithm to adaptively optimize the parameters of Variational Mode Decomposition (VMD), enabling effective separation of signal and noise. Furthermore, the Dual-head attention mechanism embedded in a Long Short-Term Memory (DLSTM) network captures long-range temporal dependencies, while the network is trained using a supervised learning method to learn the mapping from noisy Intrinsic Mode Functions (IMFs) to clean signals, ultimately achieving denoising without requiring manual component selection. To verify the superiority of LBTO-VMD-DLSTM, its performance was compared with traditional algorithms such as Empirical Mode Decomposition (EMD), Denoising Autoencoder (DAE), and Complete Ensemble Empirical Mode Decomposition with Adaptive Noise combined with Wavelet Transform (CEEMDAN-WT). The experimental results show that the proposed denoising method achieved a maximum Signal-to-Noise Ratio (SNR) of 21.75 dB and a Cosine Similarity (CosSim) of 0.99. In tests conducted on MCG signals with added noise at different SNR levels and different types of baseline drift, the LBTO-VMD-DLSTM method produced the highest SNRs (20.91 dB and 23.5 dB) and the highest CosSim values (0.99 and 0.98). This indicates that the proposed method outperforms the comparison algorithms, effectively eliminating complex noise in MCG signals while preserving waveform features critical for subsequent clinical interpretation.