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Electrocardiogram signal denoising using non-local wavelet transform domain filtering

Santosh Kumar Yadav, Rohit Sinha, Prabin Kumar Bora

arXiv:1611.03320v1stat.AP

TL;DR

ECG denoising matters because wireless recordings can acquire AWGN that must be removed for diagnosis. NLWT groups similar blocks and shrinks their 2D wavelet coefficients to exploit local and nonlocal correlations. The authors report better performance than existing methods and improved preservation of diagnostic features.

  • Problem

    Wireless ECG recordings can acquire AWGN, and the paper identifies its removal as necessary for correct diagnosis.

    Source: §I · p. 1

  • Method

    NLWT groups similar ECG sample blocks and denoises them by shrinking their 2D DWT coefficients, exploiting local and nonlocal similarity.

    Source: §I · p. 1

  • Results

    NLWT outperformed existing methods on multiple performance measures and was reported to preserve diagnostic features better.

    Source: A. Evaluation on MIT-BIH Physionet… · p. 6, §VI · p. 8

  • Takeaways & Limitations

    The authors report better preservation of diagnostic ECG features than with the existing algorithms they compared.

    Source: §VI · p. 8

    The method's reported improvement concerns white Gaussian noise; the paper frames its application around channel noise, while ECG recordings are often affected by non-Gaussian or structured noise.

    Source: §V · p. 8

Abstract

from arXiv · show

ECG signals are usually corrupted by baseline wander, power-line interference, muscle noise, etc. and numerous methods have been proposed to remove these noises. However, in case of wireless recording of the ECG signal it gets corrupted by the additive white Gaussian noise (AWGN). For the correct diagnosis, removal of AWGN from ECG signals becomes necessary as it affects the all the diagnostic features. The natural signals exhibit correlation among their samples and this property has been exploited in various signal restoration tasks. Motivated by that, in this work we propose a nonlocal wavelet transform domain ECG signal denoising method which exploits the correlations among both local and nonlocal samples of the signal. In the proposed method, the similar blocks of the samples are grouped in a matrix and then denoising is achieved by the shrinkage of its two-dimensional discrete wavelet transform coefficients. The experiments performed on a number of ECG signals show significant quantitative and qualitative improvement in denoising performance over the existing ECG signal denoising methods.

I. INTRODUCTION

ECG noise can interfere with signals used to assess cardiac conditions, and wireless transmission introduces channel noise that must be removed for diagnosis. The paper combines nonlocal similarity with transform-domain denoising to address this problem.

I. INTRODUCTION

  • ECG supports assessment of pathological conditions, but baseline wander, power-line interference, muscle noise, and channel noise can corrupt it.Wireless ambulatory recordings are sent to a remote location for analysis, and the paper identifies noise removal as necessary for correct diagnosis.Source: §I · p. 1
  • Prior ECG denoising includes DWT coefficient shrinkage and EMD; discarding early IMFs can distort QRS complexes.A Tukey window has been used to preserve QRS portions, and a hybrid EMD-wavelet method combines windowed EMD with soft-thresholding.Source: §I · p. 1
  • The proposed method denoises ECG by collaboratively shrinking 2D DWT coefficients of matrices formed from similar sample blocks, then averaging overlapping estimates.It is designed to exploit both local and nonlocal signal similarity.Source: §I · p. 1

A. Problem Formulation

  • The problem formulation models channel noise as AWGN and represents each observed sample as the clean signal plus noise.The paper states that ECG samples are correlated while AWGN samples are uncorrelated, motivating sparsifying-transform denoising.Source: A. Problem Formulation · p. 2

B. NLM Algorithm

The NLM algorithm estimates each ECG sample by weighting neighboring samples according to neighborhood similarity. The paper identifies limitations of this sample-wise approach for ECG, including its assumptions about QRS values and its handling of similar neighborhoods.

B. NLM Algorithm

  • NLM estimates a sample by weighted averaging of samples with similar local neighborhoods inside a search window.Weights reflect neighborhood similarity; the method repeats this procedure for each sample.Source: B. NLM Algorithm · p. 2
  • NLM assumes clean ECG samples with similar neighborhoods are close in value, an assumption the paper says may not hold for QRS complexes.Averaging is intended to denoise when the noise is zero-mean.Source: B. NLM Algorithm · p. 2
  • Similar samples with dissimilar neighborhoods can receive low weights, while noisy samples with similar neighborhoods can receive high weights.The paper says both patterns can lead to a noisy estimate; an estimate also does not contribute to nearby samples.Source: B. NLM Algorithm · p. 2

III. NLWT DENOISING METHOD

NLWT extends sample-wise NLM by processing overlapping blocks collaboratively and shrinking 2D wavelet coefficients across similar blocks. Denoised blocks are returned to their original locations and combined into the final signal.

III. NLWT DENOISING METHOD

  • NLWT processes overlapping blocks collaboratively, then shrinks 2D orthogonal-transform coefficients across similar blocks to exploit intra-block and inter-block correlations.The paper uses 2D DWT shrinkage and averages the multiple estimates produced for each sample.Source: §III · p. 2

A. Notations

  • A similarity data matrix (SDM) contains similar blocks as columns, with the reference block first for notational convenience.The reference block has length 2L + 1, and candidate blocks are searched within a window of size 2M + 1 using threshold τ.Source: A. Notations · p. 2

B. Proposed NLWT Algorithm

1) SDM extraction:

SDM extraction searches for blocks similar to a reference block, using a projected feature-space similarity measure. The resulting matrices collect structurally similar blocks for collaborative denoising.

1) SDM extraction:

  • PCA-based projection provides a locally learned feature space for comparing candidate blocks; the DCT is offered as a less computationally intensive alternative.A candidate is selected when its similarity measure is at or below threshold τ.Source: 1) SDM extraction · p. 3
  • Each reference block searches within a window for up to m similar blocks, and the next reference location advances by k samples.The shift is constrained to leave at least one sample of overlap between successive reference blocks.Source: 1) SDM extraction · p. 3
  • The illustrated SDM captures structural similarity among extracted blocks, and its denoised version is produced by shrinking 2D DWT coefficients.The figure shows an example from noisy ECG signal 100.Source: Figure 2 · p. 4, 1) SDM extraction · p. 4

2) Transform coefficient shrinkage:

The method denoises groups of similar ECG blocks by sparsifying their two-dimensional structure with a 2D DWT, then thresholding and reconstructing them. This shrinkage uses both local and nonlocal similarity while preserving the SDM's structural similarity.

2) Transform coefficient shrinkage:

  • Each SDM groups similar blocks, whose homogeneous structure provides redundancy for a 2D DWT sparsifying transform.The denoised SDM is reconstructed with the inverse transform after coefficient thresholding.Source: 2) Transform coefficient shrinkage · p. 4
  • The shrinkage operator is hard thresholding: coefficients with magnitude at least λ_i are retained, and the others are set to zero.λ_i is the shrinkage threshold for the corresponding SDM.Source: 2) Transform coefficient shrinkage · p. 4
  • 2D DWT coefficient shrinkage exploits both inter-row (local) and inter-column (nonlocal) similarity in each SDM.The method transforms each SDM, thresholds its coefficients, and applies the inverse transform to obtain a denoised SDM.Source: 2) Transform coefficient shrinkage · p. 4

3) Aggregation:

The method returns each block estimate to its original temporal location and combines multiple estimates of a sample using weighted averaging. It also describes the aggregation weight and lists the algorithm parameters.

3) Aggregation:

  • Each sample's multiple estimates are combined by weighted averaging after estimated blocks return to their original temporal locations.The method assumes independence among the estimated columns of each SDM when defining its aggregation weight.Source: 3) Aggregation · p. 4
  • For each sample appearing in multiple blocks from one or more SDMs, the final estimate is their weighted average; assuming independence among estimated columns, aggregation weight is chosen as the inverse variance of the denoised SDM.Source: 3) Aggregation · p. 4
  • The weighting gives less importance to estimated blocks with sharp gradients than to smoother blocks, with the stated aim of avoiding QRS-complex smoothing.Homogeneous blocks retain fewer coefficients after thresholding and therefore receive larger weights.Source: 3) Aggregation · p. 4

C. Parameters

  • The algorithm parameters include block and search-window half-widths, maximum SDM block count, matching and shrinkage thresholds, and mother-wavelet type.The passage introduces these parameters for discussion of their significance.Source: C. Parameters · p. 4

1) Block size:

Parameter choices balance the capture of ECG features and similar blocks against grouping errors and computational complexity. The method specifies considerations for block size, search range, matching threshold, and shrinkage threshold.

1) Block size:

  • Block size, parameterized by half-width L, should capture signal features; the tested range is 0.01f_s–0.1f_s, with 50% overlap (k = L).Larger blocks reduce matching chances within a search window, while smaller blocks can increase erroneous grouping and complexity.Source: 1) Block size · p. 4

2) Search window:

  • The search window spans 2M + 1 samples, limiting complexity while allowing multiple heartbeats and potentially similar QRS complexes, P-waves, and T-waves.A smaller M restricts the search to local samples; a larger M increases complexity.Source: 2) Search window · p. 4

3) Matching threshold:

  • The matching threshold τ controls how many blocks enter an SDM: too small can leave a single block, while too large can group dissimilar blocks and smooth diagnostic features.For ECG normalized to ±1 mV, the threshold is determined experimentally; the table describes tuning ranges and optimal values but supplies no values in its caption.Source: 3) Matching threshold · pp. 4–5, Table I · p. 5

4) Shrinkage threshold:

  • The shrinkage threshold is set to λ_i = c_iσ, with c_i obtained from the VisuShrink soft-thresholding formula and scaled to the SDM's coefficient count.The passage gives c_i = √2 log N_i, where N_i is the number of transform coefficients in the ith SDM.Source: 4) Shrinkage threshold · p. 5

IV. EXPERIMENTS AND RESULTS

The experiments use two ECG databases and assess denoising with three quantitative measures. The passages specify the evaluation setup and desired metric directions, but provide no comparative results.

IV. EXPERIMENTS AND RESULTS

  • The evaluation uses MIT-BIH arrhythmia records for comparisons with existing techniques and PTB diagnostic records to verify performance on ECGs with known pathology.Both databases are from PhysioNet.Source: §IV · p. 5
  • Quantitative assessment uses signal-to-noise-ratio improvement (SNRimp), mean square error (MSE), and percent root mean square difference (PRD).The measures are selected for consistency with prior works and.Source: §IV · p. 5
  • A better denoising method should have higher SNRimp and lower MSE and PRD.Source: §IV · p. 5

A. Evaluation on MIT-BIH Physionet database

On MIT-BIH Physionet signals corrupted by AWGN, NLWT outperformed existing methods across three measures and SNR levels, while its denoised waveform better resembled the clean signal than NLM's.

A. Evaluation on MIT-BIH Physionet database

  • Evaluation used seven MIT-BIH records, artificially adding AWGN at four SNR levels and averaging performance over five noise realizations.Parameters were tuned on record 100; selected settings included L = 10, M = 1000, c = 3.8, and Haar (db 2).Source: A. Evaluation on MIT-BIH Physionet… · p. 5
  • NLWT outperformed existing methods on all three performance measures at every SNR level, with a considerably larger SNR improvement; Fig. 4 summarizes dataset averages across SNR levels.At 20 dB, Fig. 3 compares methods across individual ECG signals.Source: A. Evaluation on MIT-BIH Physionet… · p. 6, Figure 3 · p. 6
  • For signal 100 at 20 dB noise, the NLWT-denoised waveform better resembled the raw signal than the NLM-denoised waveform.Fig. 5 presents raw, noisy, NLM-denoised, and proposed-method waveforms from top to bottom.Source: A. Evaluation on MIT-BIH Physionet… · p. 6, Figure 5 · p. 6

B. Evaluation on PTB diagnostic database

On pathological PTB ECGs, NLWT consistently outperformed NLM and better preserved marked diagnostic features. The discussion describes its processing trade-offs, runtime, and scope for white Gaussian noise.

B. Evaluation on PTB diagnostic database

V. DISCUSSION

  • NLWT assumes repeated similar sample blocks; its 2D wavelet-domain denoising makes the rare-patch effect less prominent than in NLM, though the effect remains.The discussion notes that suggestions in may overcome the rare-patch effect.Source: §V · p. 7
  • For 10,000 samples, NLWT took 10 seconds versus 15 seconds for the fast NLM implementation on the stated computer; the paper attributes the shorter runtime to block-based processing.The authors note that optimized NLWT code could reduce runtime further.Source: §V · p. 7
  • NLWT combines wavelet-coefficient shrinkage with NLM, but unlike the related method in, it does not use a two-stage procedure followed by empirical Wiener filtering.The discussion describes the proposed method as simpler than the method in.Source: §V · p. 7
  • The reported improvement concerns white Gaussian noise; the discussion identifies non-Gaussian or structured noise as common in ECG recordings and notes relevance to Gaussian channel noise in ambulatory tele-monitoring.For other noise types, the method can be combined with interference-rejection methods as in.Source: §V · p. 8

VI. CONCLUSION

The paper concludes that NLWT exploits local and nonlocal ECG redundancy and outperforms hybrid-EMD and NLM across multiple performance measures.

VI. CONCLUSION

  • NLWT outperforms hybrid-EMD and NLM on a number of performance measures.Source: §VI · p. 8
  • NLWT preserves diagnostic features better than the existing algorithms.Source: §VI · p. 8
  • The proposed ECG denoising method exploits both local and nonlocal signal redundancy.Source: §VI · p. 8
  • Possible extensions include using learned basis transforms instead of DWT and automatically selecting the method’s parameters.Source: §VI · p. 8
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