Wang Xian-Yu, Li Cong, Zhang Rui, Wang Liang, Tan Jin-Lin, Wang Hai
State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an, China.
Academy of Space Electronic Information Technology, Xi'an, China.
Front Neurosci. 2022 Jun 1;16:921642. doi: 10.3389/fnins.2022.921642. eCollection 2022.
At present, electroencephalogram (EEG) signals play an irreplaceable role in the diagnosis and treatment of human diseases and medical research. EEG signals need to be processed in order to reduce the adverse effects of irrelevant physiological process interference and measurement noise. Wavelet transform (WT) can provide a time-frequency representation of a dynamic process, and it has been widely utilized in salient feature analysis of EEG. In this paper, we investigate the problem of translation variability (TV) in discrete wavelet transform (DWT), which causes degradation of time-frequency localization. It will be verified through numerical simulations that TV is caused by downsampling operations in decomposition process of DWT. The presence of TV may cause severe distortions of features in wavelet subspaces. However, this phenomenon has not attracted much attention in the scientific community. Redundant discrete wavelet transform (RDWT) is derived by eliminating the downsampling operation. RDWT enjoys the attractive merit of translation invariance. RDWT shares the same time-frequency pattern with that of DWT. The discrete delta impulse function is used to test the time-frequency response of DWT and RDWT in wavelet subspaces. The results show that DWT is very sensitive to the translation of delta impulse function, while RDWT keeps the decomposition results unchanged. This conclusion has also been verified again in decomposition of actual EEG signals. In conclusion, to avoid possible distortions of features caused by translation sensitivity in DWT, we recommend the use of RDWT with more stable performance in BCI research and clinical applications.
目前，脑电图（EEG）信号在人类疾病的诊断与治疗以及医学研究中发挥着不可替代的作用。EEG信号需要进行处理，以减少无关生理过程干扰和测量噪声的不利影响。小波变换（WT）能够提供动态过程的时频表示，并且已在EEG的显著特征分析中得到广泛应用。在本文中，我们研究了离散小波变换（DWT）中的平移变异性（TV）问题，该问题会导致时频定位性能下降。通过数值模拟将验证TV是由DWT分解过程中的下采样操作引起的。TV的存在可能会导致小波子空间中特征的严重失真。然而，这种现象在科学界并未引起太多关注。冗余离散小波变换（RDWT）是通过消除下采样操作而推导出来的。RDWT具有平移不变性这一吸引人的优点。RDWT与DWT具有相同的时频模式。离散δ脉冲函数用于测试DWT和RDWT在小波子空间中的时频响应。结果表明，DWT对δ脉冲函数的平移非常敏感，而RDWT的分解结果保持不变。这一结论在实际EEG信号的分解中也再次得到了验证。总之，为避免DWT中平移敏感性可能导致的特征失真，我们建议在脑机接口研究和临床应用中使用性能更稳定的RDWT。
