28-12-2012, 05:13 PM
Nonlocal Means Denoising of ECG Signals
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Abstract
Patch-based methods have attracted significant attention
in recent years within the field of image processing for a variety
of problems including denoising, inpainting, and super-resolution
interpolation. Despite their prevalence for processing 2-D signals,
they have received little attention in the 1-D signal processing literature.
In this letter, we explore application of one such method,
the nonlocal means (NLM) approach, to the denoising of biomedical
signals. Using ECG as an example, we demonstrate that a
straightforward NLM-based denoising scheme provides signal-tonoise
ratio improvements very similar to state of the art waveletbased
methods, while giving ∼3× or greater reduction in metrics
measuring distortion of the denoised waveform.
INTRODUCTION
ACCURATE extraction of clinical parameters from noisy
biomedical signals is a critical and on-going challenge.
Many sources of signal contamination including additive highfrequency
noise, motion or muscle artifacts, and baseline wander
overlap signals of clinical interest in both time and frequency
[1]–[3]. Thus, in the process of removing these sources
of contamination, standard filtering approaches can also adversely
affect these desired signal components. For example,
low-pass filtering may suppress high-frequency noise, and also
distorts waveform spikes in electromyography (EMG) or ECG
signals [2]. Important advances in biomedical signal denoising
have been made, with a large and growing literature on wavelet
denoising [1] and other techniques [3], [4].
Parameter Selection
Here, we examine parameter selection for ECG denoising.
The key NLM parameters are the patch size, specified as a halfwidth
P (so LΔ = 2P + 1), the size of N(s), specified as a
half-widthM, and the bandwidth λ. Fig. 1 shows the geometric
parameters schematically, for 1-D patches centered on the points
s and t.
The bandwidth λ is a key parameter that controls the amount
of smoothing applied. An overly small λ will cause noise fluctuations
to have too much influence in deweighting different
patches, resulting in insufficient averaging; an overly large λ
will cause dissimilar patches to appear similar, resulting in blur.
Ville and Kocher in [7] used the SURE criterion for parameter
selection and noted that for their test set, a good overall choice
of lambda is 0.5 σ, where σ is the noise standard deviation. It
is intuitive that λ should scale by σ, as for a locally flat area,
d2 ∼ 2σ2 , as variances add. Interestingly, our results below for
ECG denoising find a result very similar to [7].
RESULTS
For simulations, we use data from the Physionet MIT-BIH
arrythymia database (www.physionet.org), for the ECG signals
numbered as 100, 103, 104, 105, 106, 115, and 215. These
recordings were sampled at 360 Hz using 11-bit A/D converters.
We processed both the actual Physionet recordings (converted
to milli volts) and the signals with the white Gaussian noise
added to achieve target signal-to-noise ratio (SNR) levels. The
signals chosen and SNR levels used in simulation are identical
to those used in [4] allowing us to compare NLM to their result
CONCLUSION
In this letter, we have applied a 1-D implementation of the
nonlocal means denoising algorithm, which has received significant
attention in image processing, to denoising of ECG signals.
The results are promising, suggesting the method can provide
denoising while minimizing signal distortion. We have noted
some limitations of the method and suggest possible avenues
for the application and improvement of the technique. Given
the success of patch-based methods in image processing, we
are optimistic that NLM and related methods may be useful in
denoising biomedical signals.