A Transform Domain SVD Filter for Suppression of Muscle Noise Artefacts in Exercise ECG's

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.