Adaptive Hyperbolic Tangent Wavelet Threshold Function for Denoising in Single-Channel EEG Attention Classification

Single-channel electroencephalography (EEG) signals have broad application prospects in attention state monitoring due to their portability and low cost. However, these signals are susceptible to noise interference, which degrades classification performance. This study proposes an Adaptive Hyperbolic Tangent Wavelet Threshold Function (AHTWTF), a novel denoising framework that dynamically adjusts thresholds according to the energy distribution of wavelet coefficients, combining the smoothness of hyperbolic tangent functions with adaptive level-specific thresholding to overcome the limitations of conventional hard/soft thresholding and mode decomposition methods. By integrating AHTWTF with an Extreme Learning Machine (ELM) classifier, we establish a joint denoising-classification pipeline. Experiments on Schulte Grid task data (12 subjects, 512 Hz sampling rate, containing physiological and environmental noise) demonstrate that AHTWTF achieves superior noise suppression by preserving critical EEG features (e.g., Alpha/Beta waves) through its energy-adaptive mechanism, while avoiding mode mixing (EMD) and over-decomposition (VMD). Under a noise intensity coefficient of 0.7, the signal-to-noise ratio (SNR) reached 6.2263, significantly higher than those of the hard thresholding (3.7064) and soft thresholding (1.4865) methods, with a 44.0%–70.2% reduction in mean squared error (MSE). For classification, AHTWTF achieved a mean AUC of 0.7911, a 14.7% improvement over the baseline, attributed to its balanced trade-off between denoising intensity and the preservation of important EEG features. These results validate AHTWTF’s robustness and highlight its potential for real-world EEG applications, particularly in portable attention monitoring systems and brain-computer interfaces.