Neuronal spikes are carriers of neural information, and high-quality recordings are critical for neural coding and brain-computer interface research. However, electrophysiological recordings are often corrupted by noise, reducing the signal-to-noise ratio (SNR) and distorting spike waveforms. Although variational mode decomposition (VMD) is suitable for non stationary neural signal processing, its performance relies heavily on manual selection of mode number $ K $ and penalty factor $\alpha$, resulting in poor adaptability. This paper proposes a neuronal spike denoising method combining tornado optimizer with Coriolis force (TOC)-optimized VMD and wavelet thresholding. With Hilbert envelope entropy as the fitness function, TOC adaptively optimizes VMD parameters; the kurtosis criterion separates signal-dominant and noise-dominant components; wavelet thresholding further denoises noise-dominant parts to reconstruct purified spike signals from valid components. Experiments on simulated and real neuronal signals verify that the proposed method outperforms classic empirical mode decomposition, conventional VMD and particle swarm optimization-VMD. Specifically, on real signals, it improves the SNR by 14.0322 dB, reduces mean absolute error by 0.0815 and root mean square error by 0.1102, raises the normalized cross-correlation by 0.0494 and the energy SNR by 6.30%. The proposed method effectively suppresses noise while preserving spike waveform features, providing high-quality data for subsequent spike sorting and neural decoding.
Citation: Can Ma, Zuozhi Liu, Hui Li. Variational mode decomposition optimized by the tornado optimization algorithm combined with wavelet thresholding for neuronal spike signal denoising[J]. AIMS Mathematics, 2026, 11(6): 17208-17238. doi: 10.3934/math.2026706
Neuronal spikes are carriers of neural information, and high-quality recordings are critical for neural coding and brain-computer interface research. However, electrophysiological recordings are often corrupted by noise, reducing the signal-to-noise ratio (SNR) and distorting spike waveforms. Although variational mode decomposition (VMD) is suitable for non stationary neural signal processing, its performance relies heavily on manual selection of mode number $ K $ and penalty factor $\alpha$, resulting in poor adaptability. This paper proposes a neuronal spike denoising method combining tornado optimizer with Coriolis force (TOC)-optimized VMD and wavelet thresholding. With Hilbert envelope entropy as the fitness function, TOC adaptively optimizes VMD parameters; the kurtosis criterion separates signal-dominant and noise-dominant components; wavelet thresholding further denoises noise-dominant parts to reconstruct purified spike signals from valid components. Experiments on simulated and real neuronal signals verify that the proposed method outperforms classic empirical mode decomposition, conventional VMD and particle swarm optimization-VMD. Specifically, on real signals, it improves the SNR by 14.0322 dB, reduces mean absolute error by 0.0815 and root mean square error by 0.1102, raises the normalized cross-correlation by 0.0494 and the energy SNR by 6.30%. The proposed method effectively suppresses noise while preserving spike waveform features, providing high-quality data for subsequent spike sorting and neural decoding.
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Can Ma, Zuozhi Liu, Hui Li. Variational mode decomposition optimized by the tornado optimization algorithm combined with wavelet thresholding for neuronal spike signal denoising[J]. AIMS Mathematics, 2026, 11(6): 17208-17238. doi: 10.3934/math.2026706
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