Electrocardiogram Signal Denoising using Nonlocal Wavelet Transform Domain Filtering

ECG signal is one of the most popular diagnostic means which provides an electrical picture of the heart and information about different pathological conditions. These signals originate from the heart and pass through the tissues with different characteristics to reach up to the several recording leads placed on the skin of the subject. Because of the path deformities and external electrical disturbances, ECG signals become noisy. The typical noises in the ECG include baseline wander, power-line interference, muscle noise, etc. In recent years, the biotelemetry has become a dominant means of monitoring the cardiac condition of ambulatory patients [1, 2]. Also, to detect arrhythmias and cardiac abnormalities, wireless ambulatory ECG recording is now routinely used [3]. In such cases, the ECG data is sent through the channel (wireless, telephone lines, etc.) to a remote location where it is analyzed. In this process, it gets corrupted by the channel noise. For the correct diagnosis, the removal of noise from such ECG signals becomes necessary. In the past, a number of algorithms have been proposed for ECG signal denoising [4, 5, 6, 7, 8, 9]. Among those, the methods based on the discrete wavelet transform (DWT) coefficient shrinkage [5, 9, 10] and the empirical mode decomposition (EMD) [4, 8] have emerged as two popular groups. In the former group, a good estimate of clean ECG signal is obtained by discarding the lower magnitude DWT coefficients followed by the inverse wavelet transform. In the latter group, the estimate of clean ECG signal is obtained by discarding first few intrinsic mode functions (IMFs) since these account for the high frequency variations present in the signal. However, this process is reported to distorts the QRS complexes. In [11] the portions of the first few IMFs those correspond to the QRS complexes are preserved by means of a Tukey window. In [12] a hybrid EMD-wavelet method that combines the windowed EMD with wavelet soft-thresholding has been proposed to further improve the denoising performance. The nonlocal means (NLM) method [13] is a very successful image denoising method. Recently, it has been applied for ECG signal denoising [14] and is shown to outperform the hybrid EMD-wavelet method for a number of ECG signals. The NLM method was originally developed for image denoising with the assumption that the underlying clean image has several pixels with similar neighborhood. In normal cases, the ECG signals are almost structurally repetitive and thus possess such redundancy. In one-dimensional NLM denoising proposed in [14], the estimates of the underlying clean signal samples are obtained by weighted averaging of the samples having similar neighborhoods. The applied weighting is proportional to the similarity in the neighborhood and is independent of the temporal location of the samples. As a result, the samples with quite similar neighborhoods are given higher weights whereas lower weights are assigned to the samples with dissimilar neighborhoods. Thus, it directly exploits the nonlocal similarity present in the signal. The NLM algorithm uses a sample-based approach in which each sample is estimated independently. In other words, the estimate of a sample at one location does not contribute to the estimation of other samples even if those are in close proximity. The nonlinear filtering methods like the shrinkage of the DWT coefficients do not face such drawback as these rely on the inherent sparsity of the clean signal in the transform domain. However, the DWT shrinkage based methods could not exploit the nonlocal redundancy present in the signal. On combining the transform based approach and the block-based NLM approach, their relative advantages can be exploited. The similar idea has already been explored for image denoising [15, 16, 17] but is yet to be explored for the biomedical signals like ECG, EEG, etc. In this paper we propose a novel ECG denoising method which exploits local as well as nonlocal similarity in the signal. In the proposed method, the similar blocks of samples are estimated in a collaborative manner. The denoising is accomplished by the shrinkage of the two-dimensional (2D) DWT coefficients of the matrix formed with these similar blocks. This process is repeated for each of the overlapping blocks resulting in several estimates for a sample. The final estimate is found by averaging these estimates. The remainder of this paper is organized as follows. In Section II, the denoising problem is formulated and the existing NLM denoising method for ECG signals is described. The details of the proposed algorithm along with the parameter tuning are given in Section III. The experimental results and discussions are presented in Section IV and Section V, respectively. Section VI concludes the paper.