Paul J S, Reddy M R, Kumar V J
Department of Electrical Engineering, Indian Institute of Technology, Chennai, India.
IEEE Trans Biomed Eng. 2000 May;47(5):654-63. doi: 10.1109/10.841337.
The proposed filter assumes the noisy electrocardiography (ECG) to be modeled as a signal of deterministic nature, corrupted by additive muscle noise artefact. The muscle noise component is treated to be stationary with known second-order characteristics. Since noise-free ECG is shown to possess a narrow-band structure in discrete cosine transform (DCT) domain and the second-order statistical properties of the additive noise component is preserved due to the orthogonality property of DCT, noise abatement is easily accomplished via subspace decomposition in the transform domain. The subspace decomposition is performed using singular value decomposition (SVD). The order of the transform domain SVD filter required to achieve the desired degree of noise abatement is compared to that of a suboptimal Wiener filter using DCT. Since the Wiener filter assumes both the signal and noise structures to be statistical, with a priori known second-order characteristics, it yields a biased estimate of the ECG beat as compared to the SVD filter for a given value of mean-square error (mse). The filter order required for performing the subspace smoothing is shown to exceed a certain minimal value for which the mse profile of the SVD filter follows the minimum-mean-quare error (mmse) performance warranted by the suboptimal Wiener filter. The effective filter order required for reproducing clinically significant features in the noisy ECG is then set by an upper bound derived by means of a finite precision linear perturbation model. A significant advantage resulting from the application of the proposed SVD filter lies in its ability to perform noise suppression independently on a single lead ECG record with only a limited number of data samples.
所提出的滤波器假设噪声心电图（ECG）被建模为具有确定性性质的信号，被加性肌肉噪声伪迹所干扰。肌肉噪声分量被视为具有已知二阶特性的平稳信号。由于无噪声ECG在离散余弦变换（DCT）域中具有窄带结构，并且由于DCT的正交性，加性噪声分量的二阶统计特性得以保留，因此可以通过变换域中的子空间分解轻松实现噪声消除。子空间分解使用奇异值分解（SVD）来执行。将实现所需噪声消除程度所需的变换域SVD滤波器的阶数与使用DCT的次优维纳滤波器的阶数进行比较。由于维纳滤波器假设信号和噪声结构均为统计性的，具有先验已知的二阶特性，因此在给定均方误差（mse）值的情况下，与SVD滤波器相比，它会产生对ECG搏动的有偏估计。对于执行子空间平滑所需的滤波器阶数，当SVD滤波器的mse曲线遵循次优维纳滤波器保证的最小均方误差（mmse）性能时，显示其超过某个最小值。然后，通过有限精度线性扰动模型得出的上限来设置在噪声ECG中再现临床显著特征所需的有效滤波器阶数。应用所提出的SVD滤波器带来的一个显著优点在于，它能够仅使用有限数量的数据样本在单导联ECG记录上独立执行噪声抑制。
