# Denoise EEG Signals Using Differentiable Signal Processing Layers

This example shows how to remove electro-oculogram (EOG) noise from electroencephalogram (EEG) signals using the *EEGdenoiseNet* benchmark data set [1] and deep learning regression. The *EEGdenoiseNet* data set contains 4514 clean EEG segments and 3400 ocular artifact segments that can be used to synthesize noisy EEG segments with the ground-truth clean EEG (the data set also contains muscular artifact segments, but these will not be used in this example).

This example uses clean and EOG-contaminated EEG signals to train a long short-term memory (LSTM) model to remove the EOG artifacts. You first train the model on the raw input signals. Then, a short-time Fourier transform (STFT) layer is introduced so that the model trains on the extracted time-frequency features of the input. An inverse STFT layer reconstructs the results from the denoised STFT. Using the time-frequency features improves performance especially at degraded SNR values.

### Create Data Set

The EEGdenoiseNet data set contains 4514 clean EEG segments and 3400 EOG segments that can be used to generate three data sets for training, validating, and testing a deep learning model. The sample rate of all the signal segments is 256 Hz. For convenience, the data set has been uploaded to this location: https://ssd.mathworks.com/supportfiles/SPT/data/EEGEOGDenoisingData.zip

Download the dataset using the `downloadSupportFile`

function.

% Download the data datasetZipFile = matlab.internal.examples.downloadSupportFile("SPT","data/EEGEOGDenoisingData.zip"); datasetFolder = fullfile(fileparts(datasetZipFile),"EEG_EOG_Denoising_Dataset"); if ~exist(datasetFolder,"dir") unzip(datasetZipFile,fileparts(datasetZipFile)); end

After downloading the data, the location in `datasetFolder`

contains two MAT files:

`EEG_all_epochs.mat`

— A matrix with 4514 clean EEG segments of length 512 samples`EOG_all_epochs.mat`

— A matrix with 3400 EOG segments of length 512 samples

Use the `createDataset`

helper function to generate training, validation, and testing data sets. The function combines clean EEG and EOG signals to generate pairs of clean and noisy EEG segments with different signal-to-noise ratios (SNR). For any EEG and EOG pair you can use the following pair of equations to obtain a noisy segment with a given SNR:

$$\mathrm{noisyEEG}=\mathrm{EEG}+\lambda \cdot \mathrm{EOG}$$

$$\mathrm{SNR}=10\cdot {\mathrm{log}}_{10}\left(\frac{\mathrm{rms}\left(\mathrm{EEG}\right)}{\mathrm{rms}\left(\lambda \cdot \mathrm{EOG}\right)}\right)$$

You vary the parameter $\lambda $ to control the artifact power and achieve a particular SNR value.

To create the training data set, `createDataset `

combines the first 2720 pairs of EEG and EOG segments ten times each with random SNRs in the [-7, 2] dB interval for a total of 27,200 training pairs. Each training pair is stored in a MAT file inside a folder named `train`

. Each MAT file includes:

A clean EEG segment (stored under a variable named

`EEG`

)An EOG segment (stored under a variable named

`EOG`

)A noisy EEG segment (stored under a variable named

`noisyEEG`

)The SNR of the noisy segment (stored under a variable named

`SNR`

)The sample rate value of the signal segments (stored under a variable named

`Fs`

)

To create the validation data set, `createDataset`

combines the next 340 pairs of the EEG and EOG segments ten times each with random SNRs in the [–7, 2] dB interval for a total of 3400 validation segments. Validation data is stored in MAT files inside a folder named `validate`

. Each MAT file contains the same variables as the ones described for the training set.

Finally, to create the test data set, `createDataset`

combines the next 340 pairs of EEG and EOG segments ten times each with deterministic SNR values of –7, –6, –5, –4, –3, –2, –1, 0, 1, and 2 dB. The test data is stored in MAT files inside a folder named `test`

. Test MAT files with the same SNR value are grouped under a common subfolder to make it easier to analyze the denoising performance of the trained model for a given SNR. For example, files with test signals with an SNR of -3 dB are stored in a folder with name `data_SNR_-3`

.

Call the `createDataset`

function to create the data set (this may take a few seconds). Set the `createDatasetFlag`

to false if you already have the data set in the `datasetFolder`

and want to skip this step.

createDatasetFlag = true; if createDatasetFlag createDataset(datasetFolder); end

### Prepare Datastores to Consume Data

The generated data set is quite large (approximately 430 MB), so it is convenient to use datastores to access the data without having to read it all at once into memory. Create signal datastores to access the training and validation data. Use the `SignalVariableNames`

parameter to specify the variables you want to read from the MAT files (in the order you want them read). Also specify the `ReadOutputOrientation`

as `"row"`

to ensure the data is compatible with the LSTM network.

ds_Train = signalDatastore(fullfile(datasetFolder,"train"), ... SignalVariableNames=["noisyEEG","EEG"], ... ReadOutputOrientation="row"); ds_Validate = signalDatastore(fullfile(datasetFolder,"validate"), ... SignalVariableNames=["noisyEEG","EEG"], ... ReadOutputOrientation="row");

Read the data from the first training file and plot the clean and noisy EEG signals. A call to preview or read methods of the datastore yields a 1-by-2 cell array with the first element containing a noisy EEG segment, and the second element containing a clean EEG segment.

data = preview(ds_Train); plot([data{2} data{1}],LineWidth=2) legend("Clean EEG","EEG with EOG artifact") axis tight

The performance of a regression network is usually improved if the input and output signals are normalized. You can transform the signal datastores to apply normalization to each signal as it is read from disk. The `normalizeData`

helper function is listed at the end of this example. It simply subtracts the signal mean and divides the result by the signal's standard deviation.

ds_Train_T = transform(ds_Train,@normalizeData); ds_Validate_T = transform(ds_Validate,@normalizeData);

### Train Regression Model to Denoise EEG Signals

Train a network to denoise signals by passing noisy EEG signals into the network input and requesting the desired EEG clean ground-truth signals at the network output. A long-short term memory (LSTM) architecture is chosen because it is capable of learning features from time sequences.

Define the network architecture: the number of features is set to one as a single sequence is input to the network and a single sequence is output from the network. Use a dropout layer to reduce overfitting of the model on the training data. Note that normalization must be applied to input and output signals so it is more convenient to use transformed datastores than to use the `Normalization`

option of the `sequenceInputLayer`

that only normalizes the inputs.

numFeatures = 1; numHiddenUnits = 100; layers = [ sequenceInputLayer(numFeatures) lstmLayer(numHiddenUnits) dropoutLayer(0.2) fullyConnectedLayer(numFeatures) ];

Define the training option parameters: use an Adam optimizer and choose to shuffle the data at every epoch. Display the training progress in a plot and monitor the root mean squared error. Also, specify the validation datastore `ds_Validate_T`

as the source for the validation data.

maxEpochs = 5; miniBatchSize = 150; options = trainingOptions("adam", ... Metrics="rmse", ... MaxEpochs=maxEpochs, ... MiniBatchSize=miniBatchSize, ... InitialLearnRate=0.005, ... GradientThreshold=1, ... Plots="training-progress", ... Shuffle="every-epoch", ... Verbose=false, ... ValidationData=ds_Validate_T, ... ValidationFrequency=100, ... OutputNetwork="best-validation-loss");

Use the `trainnet`

function to train the model. Specify `"mse"`

as the loss function. You can directly pass the transformed training datastore into the function because the datastore outputs a 1-by-2 cell array, with input and output signals, at each call to the `read`

method.

The training steps will take several minutes. You can skip these steps by downloading the two pretrained networks, `rawNet`

and `stftNet`

, using the selector below. If you want to train the network as the example runs, select '`Train networks`

'. If you want to skip the training steps and download a MAT file containing the pretrained networks, select '`Download Networks`

'.

trainingFlag = "Train networks"; if trainingFlag == "Train networks" rawNet = trainnet(ds_Train_T,layers,"mse",options); else % Download the pretrained networks modelsZipFile = matlab.internal.examples.downloadSupportFile("SPT","data/EEGEOGDenoisingNetworks.zip"); modelsFolder = fullfile(fileparts(modelsZipFile),"EEG_EOG_Denoising_Networks"); if ~exist(modelsFolder,"dir") unzip(modelsZipFile,fileparts(modelsZipFile)); end modelsFile = fullfile(modelsFolder,"trainedNetworks.mat"); load(modelsFile) end

### Analyze Denoising Performance of Trained Model

Use the test data set to analyze the denoising performance of the `rawNet`

network. Recall that the test data set contains multiple test files for each SNR value in [–7, –6, –5, –4, –3, –2, –1, 0, 1, 2] dB. The performance metric is chosen as the mean-squared error (MSE) between the clean baseline EEG signal and the denoised EEG signal. The MSE of the clean EEG signal and the noisy EEG signal is also computed to show the worst-case MSE when no denoising is applied. At each SNR, compute 340 MSE values for each of the 340 available test EEG segments and obtain the average MSE.

Create a `signalDatastore`

to consume the test data and use a transformed datastore to setup data normalization. Since the data is now inside subfolders of the test folder, specify `IncludeSubfolders`

as `true`

. Further, use the `folders2labels`

function to get the list of folder names for each file in the test data set so that you can get data for each SNR.

ds_Test = signalDatastore(fullfile(datasetFolder,"test"), ... SignalVariableNames=["noisyEEG","EEG"], ... IncludeSubfolders=true, ... ReadOutputOrientation="row"); ds_Test_T = transform(ds_Test,@normalizeData); % Get labels that contain the SNR value for each file in the datastore labels = folders2labels(ds_Test); unique(labels)

`ans = `*10×1 categorical*
data_SNR_-1
data_SNR_-2
data_SNR_-3
data_SNR_-4
data_SNR_-5
data_SNR_-6
data_SNR_-7
data_SNR_0
data_SNR_1
data_SNR_2

For each SNR value, denoise the test signals and compute the average MSE value. Use the `subset`

function of the datastore to get a datastore pointing to the data for each SNR. To denoise a signal, call the `minibatchpredict`

function. Pass the trained network and the noisy data as inputs to `minibatchpredict`

.

SNRs = (-7:2); MSE_Denoised_rawNet = zeros(numel(SNRs),1); % Measure denoising performance MSE_No_Denoise = zeros(numel(SNRs),1); % Measure worst-case MSE when no denoising is applied for idx = 1:numel(SNRs) lblIdx = find(labels == "data_SNR_"+num2str(SNRs(idx))); ds_Test_SNR = subset(ds_Test_T,lblIdx); % New datastore pointing to files with current SNR value % Denoise the data using the minibatchpredict function of the trained model pred = minibatchpredict(rawNet,ds_Test_SNR,UniformOutput=false); % Use a signal datastore to loop over the 340 denoised signals for the % current SNR value. Transform the datastore to add the normalization % step. ds_Pred = transform(signalDatastore(pred),@normalizeData); mse = 0; mseWorstCase = 0; cnt = 0; while hasdata(ds_Pred) testData = read(ds_Test_SNR); denoisedData = read(ds_Pred); % MSE performance of denoiser - testData{2} contains clean EEG, % testData{1} contains noisy EEG. mse = mse + sum((testData{2} - denoisedData).^2)/numel(denoisedData); % Worst-case MSE performance when no denoising is applied. % Convert data to single precision as denoisedData is single % precision. mseWorstCase = mseWorstCase + sum((single(testData{2}) - single(testData{1})).^2)/numel(testData{1}); cnt = cnt+1; end % Average MSE of denoised signals MSE_Denoised_rawNet(idx) = mse/cnt; % Worst-case average MSE MSE_No_Denoise(idx) = mseWorstCase/cnt; end

Plot the average MSE results.

figure plot(SNRs,[MSE_No_Denoise,MSE_Denoised_rawNet],LineWidth=2) xlabel("SNR") ylabel("Average MSE") title("Denoising Performance") legend("Worst-case scenario (no-denoising)","Denoising with rawNet model")

### Improve Performance Using Short-Time Fourier Transform Feature Extraction

A common approach to improve performance of a deep learning model is to train using features of the input signal data. The features provide a representation of the input data that makes it easier for the network to learn the most important aspects of the signals.

Choose a short-time Fourier transformation (STFT) with a window length of 64 samples and overlap length of 63 samples. This transformation will effectively create 33 complex features with a length of 449 samples each.

winLength = 64; overlapLength = 63;

Compute and plot the STFT of a pair of clean and noisy EEG signals that have been normalized.

data = preview(ds_Train_T); plotSTFT(data,winLength,overlapLength)

The idea is to train a network so that it can produce a denoised signal based on the STFT of the noisy input signal.

Modify the existing network. Insert a STFT layer so that the network obtains the STFT of the input data. Set the layer transform mode to `"realimag"`

. The layer concatenates the real and imaginary parts of the STFT in the channel dimension of the layer output. To reconstruct the signal from the denoised STFT obtained by the network, insert an ISTFT layer after the fully connected layer. Set the output size of the fully connected layer to `66`

, so that the output size of the ISTFT layer matches the input size to the STFT layer.

minLen=512; % signal length numFeatures=66; % number of features win=rectwin(winLength); % analysis window layers = [ sequenceInputLayer(1,MinLength=minLen) stftLayer(Window=win,OverlapLength=overlapLength,transform="realimag") lstmLayer(numHiddenUnits) dropoutLayer(0.2) fullyConnectedLayer(numFeatures) istftLayer(Window=win,OverlapLength=overlapLength) ];

Train the network if `trainingFlag`

is `"Train networks"`

.

if trainingFlag == "Train networks" stftNet = trainnet(ds_Train_T,layers,"mse",options); end

Use the trained network to denoise EEG signals using the test data. Compute average MSE values by comparing denoised and clean baseline EEG signals.

MSE_Denoised_stftNet = zeros(numel(SNRs),1); % Measure denoising performance for idx = 1:numel(SNRs) lblIdx = find(labels == "data_SNR_"+num2str(SNRs(idx))); % New datastores pointing to files with current SNR value ds_Test_SNR = subset(ds_Test_T,lblIdx); % Raw EEG signals to compute MSE % Denoise the data using the predict function of the trained model. pred = minibatchpredict(stftNet,ds_Test_SNR,UniformOutput=false); % Use a signal datastore to loop over the 340 denoised signals for the % current SNR value. ds_Pred = signalDatastore(pred); mse = 0; cnt = 0; while hasdata(ds_Pred) testData = read(ds_Test_SNR); denoisedData = read(ds_Pred); % MSE performance of denoiser - testData{2} contains clean EEG mse = mse + sum((testData{2}(:) - denoisedData(:)).^2)/numel(denoisedData); cnt = cnt+1; end % Average MSE of denoised signals MSE_Denoised_stftNet(idx) = mse/cnt; end

Plot the average MSE obtained with no denoising, denoising with a network trained with raw input signals, and denoising with a network trained with STFT transformed signals. You can see that the addition of the STFT step has improved the performance especially at the lower SNR values.

figure plot(SNRs, ... [MSE_No_Denoise,MSE_Denoised_rawNet,MSE_Denoised_stftNet], ... LineWidth=2) xlabel("SNR") ylabel("Average MSE") title("Denoising Performance") legend("Worst-case scenario (no denoising)", ... "Denoising with rawNet model", ... "Denoising with stftNet model")

Plot noisy and denoised signals for different SNRs. The `getRandomEEG`

helper function listed at the end of this example gets a random EEG signal with a specified SNR from the test dataset.

SNR = -7; % dB data = getRandomEEG(datasetFolder,SNR); noisyEEG = normalizeData(data{1}); cleanEEG = normalizeData(data{2}); denoisedEEG = minibatchpredict(stftNet,noisyEEG); plot([cleanEEG denoisedEEG noisyEEG],LineWidth=2) title("EEG denoising (SNR = " + SNR + " dB)") legend("Clean EEG", "Denoised EEG","Noisy EEG") axis tight

### Conclusion

In this example you learned how to train a deep network to perform regression for signal denoising. You compared two models, one trained with raw clean and noisy EEG signals, the other trained with features extracted using a short-time Fourier transform layer. You configured the STFT layer to handle the complex concatenation for you, enabling the network to treat the real and imaginary components as independent real features. You learned that you can use an inverse STFT layer to reconstruct the results from the denoised STFT obtained by the network. The use of STFT sequences provides greater performance improvement at worse SNRs and both approaches converge in performance as the SNR improves.

### References

[1] Haoming Zhang, Mingqi Zhao, Chen Wei, Dante Mantini, Zherui Li, Quanying Liu. "A benchmark dataset for deep learning solutions of EEG denoising." https://arxiv.org/abs/2009.11662

### Helper Functions

** normalizeData** - this function normalizes input signals by subtracting the mean and dividing by the standard deviation.

function y = normalizeData(x) % This function is only intended to support examples in Signal % Processing Toolbox. It may be changed or removed in a future release. if iscell(x) y = cell(1,numel(x)); y{1} = (x{1}-mean(x{1}))/std(x{1}); if numel(x) == 2 y{2} = (x{2}-mean(x{2}))/std(x{2}); end else y = (x - mean(x))/std(x); end end

** plotSTFT** - this function plots the short-time Fourier transform (STFT) of the input data. It converts the complex STFT results into a real matrix by concatenating the real and imaginary components.

function plotSTFT(data,winLength,overlapLength) % This function is only intended to support examples in Signal % Processing Toolbox. It may be changed or removed in a future release. dataNoisy = data{1}; dataClean = data{2}; y = stft([dataNoisy dataClean],Window=rectwin(winLength), ... OverlapLength=overlapLength, ... FrequencyRange="onesided"); stftNoisy = y(:,:,1); stftClean = y(:,:,2); tiledlayout(2,1) nexttile h = imagesc([real(stftNoisy) imag(stftNoisy)]); h.Parent.CLim = [-40 57]; title("STFT of Noisy EEG Signal") nexttile h = imagesc([real(stftClean) imag(stftClean)]); h.Parent.CLim = [-40 57]; title("STFT of Clean EEG Signal") end

** createDataset** - this function combines clean EEG signal segments with EOG segments to create training, validation and testing datasets to train an EEG denoiser neural network.

function createDataset(dataDir) % This function is only intended to support examples in Signal % Processing Toolbox. It may be changed or removed in a future release. % Create training, validation, and testing datasets consisting of clean EEG % signals and noisy EEG signals contaminated by EOG segments. load(fullfile(dataDir,"EEG_all_epochs.mat"),"EEG_all_epochs"); load(fullfile(dataDir,"EOG_all_epochs.mat"),"EOG_all_epochs"); EEG_all_epochs = EEG_all_epochs(1:3400,:).'; EOG_all_epochs = EOG_all_epochs.'; Fs = 256; trainingPercentage = 80; validationPercentage = 10; N = size(EEG_all_epochs,2); % Create a training dataset consisting of mat files containing two signals % - a clean EEG signal, and an EEG signal contaminated by EOG artifacts. % Combine each of 2720 pairs of EEG and EOG segments ten times with random % SNRs in the range -7dB to 2dB to obtain 27200 training segments. EEG_training = EEG_all_epochs(:,1:N*trainingPercentage/100); EOG_training = EOG_all_epochs(:,1:N*trainingPercentage/100); M = size(EEG_training,2); cnt = 0; if ~exist(fullfile(dataDir,"train"),'dir') mkdir(fullfile(dataDir,"train")) end for idx = 1:M for kk = 1:10 cnt = cnt + 1; EEG = EEG_training(:,idx); EOG = EOG_training(:,idx); [noisyEEG,SNR] = createNoisySegment(EEG,EOG,[-7,2]); save(fullfile(dataDir,"train", ... "data_" + num2str(cnt) + ".mat"), ... "EEG","EOG","noisyEEG","Fs","SNR"); end end % Create a validation dataset by combining 340 pairs of EEG and EOG % segments ten times with random SNRs in (-7:2) dB tPer = trainingPercentage/100; vPer = validationPercentage/100; EEG_validation = EEG_all_epochs(:,1+N*tPer:N*tPer+N*vPer); EOG_validation = EOG_all_epochs(:,1+N*tPer:N*tPer+N*vPer); M = size(EEG_validation,2); cnt = 0; if ~exist(fullfile(dataDir,"validate"),'dir') mkdir(fullfile(dataDir,"validate")) end for idx = 1:M for kk = 1:10 cnt = cnt + 1; EEG = EEG_validation(:,idx); EOG = EOG_validation(:,idx); [noisyEEG,SNR] = createNoisySegment(EEG,EOG,[-7,2]); save(fullfile(dataDir,"validate", ... "data_" + num2str(cnt) + ".mat"), ... "EEG","EOG","noisyEEG","Fs","SNR"); end end % Create a test dataset by combining 340 pairs of EEG and EOG segments ten % times with 10 SNR values [-7 -6 -5 -4 -3 -2 -1 0 1 2] dB. Store the % training sets in folders with names that identify the SNR value so that % it is easy to analyze performance by accessing files with a specific SNR. EEG_test = EEG_all_epochs(:,1+N*tPer+N*vPer:end); EOG_test = EOG_all_epochs(:,1+N*tPer+N*vPer:end); M = size(EEG_test,2); SNRVect = (-7:2); for kk = 1:numel(SNRVect) cnt = 0; if ~exist(fullfile(dataDir,"test","data_SNR_" + num2str(SNRVect(kk))),'dir') mkdir(fullfile(dataDir,"test","data_SNR_" + num2str(SNRVect(kk)))); end for idx = 1:M cnt = cnt + 1; EEG = EEG_test(:,idx); EOG = EOG_test(:,idx); [noisyEEG,SNR] = createNoisySegment(EEG,EOG,SNRVect(kk)); save(fullfile(dataDir,"test", ... "data_SNR_" + num2str(SNR)+"/" + "data_"+num2str(cnt) + ".mat"), ... "EEG","EOG","noisyEEG","Fs","SNR"); end end end function [y,SNROut] = createNoisySegment(eeg,artifact,SNR) % Combine EEG and artifact signals with a specified SNR in dB. If SNR is a % two-element vector, its value is chosen randomly from a uniform % distribution over the interval [SNR(1) SNR(2)] if numel(SNR) == 2 SNR = SNR(1) + (SNR(2)-SNR(1)).*rand(1,1); end k = 10^(SNR/10); lambda = (1/k)*rms(eeg)/rms(artifact); y = eeg + lambda * artifact; SNROut = SNR; end

** getRandomEEG** - this function reads the data from a random EEG test file with a specified SNR.

function data = getRandomEEG(datasetFolder,SNR) sds = signalDatastore(fullfile(datasetFolder,"test","data_SNR_"+num2str(SNR)), ... SignalVariableNames=["noisyEEG","EEG"],IncludeSubfolders=true); n = numel(sds.Files); idx = randi(n,1); data = read(subset(sds,idx)); end

## See Also

### Objects

### Functions

`folders2labels`

|`trainnet`

(Deep Learning Toolbox)