To view the plugin source code, please visit the plugin’s GitHub repository.

# CleanLine

Welcome to the CleanLine plugin for EEGLAB!

This plugin adaptively estimates and removes sinusoidal (e.g. line) noise from your ICA components or scalp channels using multi-tapering and a Thompson F-statistic.

CleanLine is written by Tim Mullen (tim@sccn.ucsd.edu) with thanks to Makoto Miyakoshi for beta testing. CleanLine makes use of functions modified from the Mitra Lab’s Chronux Toolbox (www.chronux.org).

CleanLine also makes use of the arg() functionality from Christian Kothe’s BCILAB toolbox (sccn.ucsd.edu/wiki/BCILAB)

# Instalation

Installation of CleanLine is simple:

1) download CleanLine (if you are reading this, you have probably already completed this step)

2) Unzip the package and copy to

3) If using the EEGLAB GUI you may start CleanLine from Tools–>CleanLine. Alternately, you can start CleanLine from the command line

```
EEGclean = pop_cleanline(EEG);
```

See “Command-line example” section below for command-line example and other parameters

5) For Help, type

```
doc cleanline
```

Or, hold mouse over any textbox, checkbox, etc in the GUI for tooltip help text.

# Theory

Sinusoidal noise can be a prominent artifact in recorded electrophysiological data. This can stem from AC power line fluctuations (e.g. 50/60 Hz line noise + harmonics), power suppliers (e.g. in medical equipment), fluorescent lights, etc. Notch filtering is generally undesirable due to creation of band-holes, and significant distortion of frequencies around the notch frequency (as well as phase distortion at other frequencies and Gibbs rippling in the time-domain). Other approaches for sinusoidal (“line”) noise reduction include adaptive regressive filtering approaches (e.g. RLS, LMS), but these typically require a reference signal (e.g. externally-recorded noise reference), which is often unavailable. Blind-source separation approaches such as ICA may help mitigate line noise, but

often fail to completely remove the noise due to spatiotemporal non-stationarities in the noise.

CleanLine uses an approach for line noise removal advocated by Partha Mitra and Hemant Bokil in “Observed Brain Dynamics” (2007), Chapter 7.3.4.

In brief, the data is traversed by a sliding window. Within each window, the signal is transformed to the frequency domain using a multi-taper FFT. The complex amplitude (amplitude and phase) is thus obtained for each frequency. Under the assumption of a deterministic sinusoid embedded in white noise, we can set up a regression of the multi-taper transform (spectrum) of this sinusoidal signal onto the multitaper spectrum of the original data at a given frequency. The regression coefficient is a complex number representing the complex amplitude (phase and amplitude) of the deterministic sinusoid. From this, a time-domain representation of the sinusoid may be constructed and subtracted from the data to remove the line.

Typically, one does not know the exact line frequency. For instance, in the U.S.A., power line noise is not guaranteed to be at exactly 60 Hz (or even to have constant phase over a given period of time). To ameliorate this problem a Thompson F-Test may be applied to determine the statistical significance of a non-zero coefficient in the above regression (indicating a sinusoid with significantly non-zero amplitude). We can then search within a narrow band around the expected location of the line for the frequency which maximizes this F-statistic above a significance threshold (e.g. p=0.05).

Line frequency scanning can be enabled/disabled using the ‘ScanForLines’ option.

Overlapping short (e.g. 2-4 second) windows can be used to adaptively estimate the frequency, phase, and amplitude of the sinusoidal noise components (which typically change over the course of a recording session). The discontinuity at the point of window overlap can be smoothed using a sigmoidal function. The example below demonstrates such a function for different smoothing factors (slope of the sigmoid).

```
winsize = 4; % window length in seconds
winstep = 2; % window step in seconds (50% overlap)
Fs = 128; % sampling rate
tau = [1 10 100]'; % smoothing factors
overlap = winsize-winstep;
toverlap = -overlap/2:(1/Fs):overlap/2;
% specify the smoothing function
foverlap = 1-1./(1+exp(-repmat(tau,1,length(toverlap)).*repmat(toverlap,length(tau),1)/overlap));
% define some colours
yellow = [255, 255, 25]/255;
red = [255 0 0]/255;
h = zeros(1,3+length(tau));
% plot the figure
figure;
axis([-winsize+overlap/2 winsize-overlap/2 0 1]); set(gca,'ColorOrder',[0 0 0; 0.7 0 0.8; 0 0 1],'fontsize',11);
hold on
h(1)=hlp_vrect([-winsize+overlap/2 -overlap/2], 'yscale',[0 1],'patchProperties',{'FaceColor',yellow, 'FaceAlpha',1,'EdgeColor','none','EdgeAlpha',0.5});
h(2)=hlp_vrect([overlap/2 winsize-overlap/2], 'yscale',[0 1],'patchProperties',{'FaceColor',red, 'FaceAlpha',1,'EdgeColor','none','EdgeAlpha',0.5});
h(3)=hlp_vrect([-overlap/2 overlap/2], 'yscale',[0 1],'patchProperties',{'FaceColor',(yellow+red)/2,'FaceAlpha',1,'EdgeColor','none','EdgeAlpha',0.5});
h(4:end) = plot(toverlap,foverlap,'linewidth',2);
plot(toverlap,1-foverlap,'linewidth',1,'linestyle','--');
hold off;
xlabel('Time (sec)'); ylabel('Smoothing weight');
title('Plot of window overlap smoothing function vs. time for different smoothing factors');
legend(h,[{'Window 1','Window 2','Overlap'},cellstr(num2str(tau))']);
```

The smoothing factor is determined by the ‘SmoothingFactor’ parameter in cleanline().

CleanLine allows you to specify the multi-taper frequency resolution by the ‘Bandwidth’ parameter. This is the width of a peak in the spectrum for a sinusoid at given frequency. Due to the time-frequency uncertainty principle, decreasing bandwidth increases the necessary length of the sliding window in order to obtain a reasonable frequency decomposition. The number of tapers, K, used by CleanLine is given by K=2TW-1 where T is the temporal resolution in seconds (window length) and W is the frequency resolution (Bandwidth) in Hz. CleanLine fixes T to be the sliding window length, so W (Bandwidth) is the only required parameter. If the ‘Verbosity’ option is set to 1, then CleanLine will display the multi-taper parameters in the command line on execution of the function.

# Tips on running CleanLine

The default options should work quite well, but parameters may need to be tweaked depending on the setup. If you have multiple epochs you need to make sure that your window size and step size exactly divides the epoch length. In other words, you do not want any sliding windows to overlap two epochs since line noise phase and amplitude may shift at that point, making it impossible to perform the time-domain line subtraction. If you have relatively short epochs (e.g. < 5 sec) it is best if each window is taken to be the length of the epoch and the step size is equal to the window length. In this way, the lines are estimated and removed for each epoch individually. When using the GUI, the default values for window length and step size are automatically set to the epoch length.

If cleaning continuous, un-epoched data, then you may wish to use sliding windows of 3-4 seconds with 50% overlap.

If using the EEGLAB GUI, commands are stored in EEG.history so that the eegh() command will return the command-line function call corresponding to the last GUI execution of CleanLine.

You might find it useful to try the option (‘PlotFigures’,true) on a subset of channels/components to get a sense of the performance of CleanLine for difference parameter choices (and also to identify where the most significant lines lie in the spectrum) and then, once you are satisfied with the parameters, turn this option off before cleaning all the remaining channels/components. NOTE: CleanLine is *considerably slower* if PlotFigures is enabled. If you don’t care to see the visualize the final results of the cleaning operation, you may also wish to set (‘ComputeSpectralPower’,false) which will speed up computation considerably.

# Typical command-line example (Multiple trials)

```
% This will run cleanline on all channels, scanning for lines +/- 1 Hz around the 60 and 120 Hz frequencies.
% Each epoch will be cleaned individually and epochs containing lines that are significantly sinusoidal at
% the p<=0.01 level will be cleaned.
EEG = pop_cleanline(EEG, 'Bandwidth',2,'ChanCompIndices',[1:EEG.nbchan] ,'SignalType','Channels','ComputeSpectralPower',true,'LineFrequencies',[60 120] ,'NormalizeSpectrum',false,'LineAlpha',0.01,'PaddingFactor',2,'PlotFigures',false,'ScanForLines',true,'SmoothingFactor',100,'VerbosityLevel',1,'SlidingWinLength',EEG.pnts/EEG.srate,'SlidingWinStep',EEG.pnts/EEG.srate);
```

# Help for cleanline.m (These can also be passed to pop_cleanline)

## Function input

**LineFrequencies:** Line noise frequencies to remove

Input Range : Unrestricted

Default value: 60 120

Input Data Type: real number (double)

**ScanForLines:** Scan for line noise

This will scan for the exact line frequency in a narrow range around the specified LineFrequencies

Input Range : [true false]

Default value: true

Input Data Type: boolean

**LineAlpha:** p-value for detection of significant sinusoid

Input Range : [0 1]

Default value: 0.01

Input Data Type: real number (double)

**Bandwidth:** Bandwidth (Hz)

This is the width of a spectral peak for a sinusoid at fixed frequency. As such, this defines the

multi-taper frequency resolution.

Input Range : Unrestricted

Default value: 1

Input Data Type: real number (double)

**SignalType:** Type of signal to clean

Cleaned ICA components will be backprojected to channels. If channels are cleaned, ICA activations

are reconstructed based on clean channels.

Possible values: ‘Components’,’Channels’

Default value : ‘Components’

Input Data Type: string

**ChanCompIndices:** IDs of Chans/Comps to clean

Input Range : Unrestricted

Default value: 1:152

Input Data Type: any evaluable Matlab expression.

**SlidingWinLength:** Sliding window length (sec)

Default is the epoch length.

Input Range : [0 4]

Default value: 4

Input Data Type: real number (double)

**SlidingWinStep:** Sliding window step size (sec)

This determines the amount of overlap between sliding windows. Default is window length (no

overlap).

Input Range : [0 4]

Default value: 4

Input Data Type: real number (double)

**SmoothingFactor:** Window overlap smoothing factor

A value of 1 means (nearly) linear smoothing between adjacent sliding windows. A value of Inf means

no smoothing. Intermediate values produce sigmoidal smoothing between adjacent windows.

Input Range : [1 Inf]

Default value: 100

Input Data Type: real number (double)

**PaddingFactor:** FFT padding factor

Signal will be zero-padded to the desired power of two greater than the sliding window length. The

formula is NFFT = 2^nextpow2(SlidingWinLen*(PadFactor+1)). e.g. For SlidingWinLen = 500, if PadFactor = -1,

we do not pad; if PadFactor = 0, we pad the FFT to 512 points, if PadFactor=1, we pad to 1024 points etc.

Input Range : [-1 Inf]

Default value: 2

Input Data Type: real number (double)

**ComputeSpectralPower:** Visualize Original and Cleaned Spectra

Original and clean spectral power will be computed and visualized at end of processing

Input Range : [true false]

Default value: true

Input Data Type: boolean

**NormalizeSpectrum:** Normalize log spectrum by detrending (not generally recommended)

Input Range : [true false]

Default value: false

Input Data Type: boolean

**VerboseOutput:** Produce verbose output

Input Range : [true false]

Default value: true

Input Data Type: boolean

**PlotFigures:** Plot Individual Figures

This will generate figures of F-statistic, spectrum, etc for each channel/comp while processing

Input Range : [true false]

Default value: false

Input Data Type: boolean

## Output Information

**EEG** Cleaned EEG dataset

**Sorig** Original multitaper spectrum for each component/channel

**Sclean** Cleaned multitaper spectrum for each component/channel

**f** Frequencies at which spectrum is estimated in Sorig, Sclean

**amps** Complex amplitudes of sinusoidal lines for each window (line time-series for window i can be reconstructed by creating a sinuoid with frequency f{i} and complex amplitude amps{i})

**freqs** Exact frequencies at which lines were removed for each window (cell array)

**g** Parameter structure. Function call can be replicated exactly by calling » cleanline(EEG,g);

# CleanLine versions

V1 - Original version by Tim Mullen

V2 - Include a rewrite by Kay Robbins with integration by Arnaud Delorme and testing by Makoto Miyakoshi