Method for realizing functional near-infrared artifact removal of self-encoder based on long and short-term memory

Abstract

The invention relates to the field of biomedical data processing, in particular to a method for realizing functional near-infrared artifact removal by an auto-encoder based on long and short term memory, which is used for processing original near-infrared signals in three stages: 1) extracting morphological characteristics of the original near-infrared signals through a down-sampling module; 2) a long and short term memory module captures time correlation between single samples to enhance features; and 3) the up-sampling module recovers and reconstructs the morphological characteristic information of the near-infrared signal from the potential space. And finally, outputting the reconstructed pure near-infrared signal at an output layer. According to the method, the defect that a traditional motion artifact removal method for signal processing excessively depends on professional knowledge and optimal selection of model parameters of a brain area is overcome, full-automatic removal of the motion artifacts is achieved, and the result shows that the method obtains good denoising results on different data sets.

Description

Technical Field

[0001] The present invention relates to the field of biomedical data processing, and in particular to a method for realizing functional near-infrared artifact removal based on a long short-term memory autoencoder. Background Art

[0002] Functional near-infrared spectroscopy (fNIRS) is a non-invasive, non-ionizing method for monitoring and imaging cerebral hemodynamic function. It uses infrared light with wavelengths in the near-infrared range (e.g., 760 and 850 nm) emitted from a source to brain tissue to measure changes in hemodynamic responses associated with neuronal activity in the brain, and uses the modified Beer-Lambert law to convert into changes in the concentrations of oxyhemoglobin (HBO) and deoxyhemoglobin (HBr), which are interpreted as the magnitude of neuronal activation in the superficial layers of the cortex. The low cost and low invasiveness of near-infrared have made it increasingly used in clinical and experimental settings for different populations. However, when subjects move their heads, the source or detector (optode) may be displaced or decoupled from the scalp, resulting in motion artifacts caused by sudden changes in light intensity. Although good coupling methods between the optical fiber and the scalp can strongly attenuate these effects, it is difficult to completely avoid these artifacts. Motion artifacts are more dramatic in populations with more and extreme head movements, such as young children and infants, and are particularly true in studies testing atypical patterns of neural activity in groups with elevated levels of head movement, such as autism spectrum disorder, attention-deficit / hyperactivity disorder, and epilepsy.

[0003] Several motion correction algorithms have been developed to prevent data loss. PCA assumes that the activation signal is orthogonal to the spatial interference pattern in the baseline data, and separates the activity-evoked response and physiological interference in diffuse optical imaging data through spatial feature filtering. Since hemodynamic responses can appear on multiple channels simultaneously, conventional PCA may accidentally remove the desired signal from the data. tPCA is an extension of PCA to prevent overcorrection. It only targets the data period with motion artifacts, but this method is more complicated to use and requires the user to manually set multiple parameters. Sample interpolation uses moving standard deviation and spline interpolation to model noisy data, which can semi-automatically detect and reduce motion artifacts in the data. This method relies on manually setting the optimal parameters, and the variance of the motion artifact must be greater than the variance of the physiological signal component. In wavelet filtering, the measured signal is first decomposed on a wavelet basis, and the wavelet coefficients that are considered to represent artifacts are zeroed before reconstructing the signal based on the corrected coefficient set. Wavelet filtering is very effective in removing spike signals, but is less effective in removing baseline shifts, and the effectiveness of wavelet filtering in removing artifacts is strongly affected by the signal-to-noise ratio of the original data.

[0004] The above algorithms all perform well in removing motion artifacts from near-infrared signals. However, the performance of these algorithms is overly dependent on the choice of model parameters and basis. In addition, traditional signal processing methods use linear relationships to establish a linear relationship between noisy signals and pure signals, while the nonlinear and non-stationary parts in deeper layers of the signal are difficult to map using this method. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings of the prior art and propose a method for functional near-infrared artifact removal based on a long short-term memory autoencoder, which overcomes the shortcomings of traditional signal processing motion artifact removal methods that are overly dependent on professional knowledge and the optimal selection of model parameters of brain regions, and realizes fully automatic removal of motion artifacts.

[0006] In order to achieve the above object, the technical solution specifically adopted by the present invention is as follows:

[0007] The method for implementing functional near-infrared artifact removal based on long short-term memory autoencoder includes the following steps:

[0008] Step 1, collecting the execution action data of multiple subjects, including: multiple subjects reading aloud, nodding up and down, nodding to the side, twisting the upper body to the right, twisting the upper body to the left, shaking the head left and right quickly, and raising eyebrows to generate motion artifacts;

[0009] Step 2: Split the data set into training set, validation set, and test set in a ratio of 8:1:1;

[0010] Step 3: Construct an autoencoder model based on long short-term memory. The denoising module of the autoencoder model consists of a downsampling module, a long short-term memory module, and an upsampling module. The calculation process of the long short-term memory module consists of the following steps:

[0011] f t =σ(W f ·[h t-1 ,θ t ]+b f )

[0012] i t =σ(W i ·[h t-1 ,θ t ]+b i )

[0013]

[0014] In the formula, f t ,i t , represents the forget gate, the input gate and represents the new cell state created using tanh, W represents the weight matrix, b f , b i , b c They represent the bias parameters of the forget gate, input gate and cell state respectively; σ represents the sigmoid activation function, and the output value is between 0 and 1; tanh represents the hyperbolic tangent activation function, and the output value is between -1 and 1; h t-1 represents the hidden state of the previous time step, C t-1 represents the cell state at the previous time step, C t Represents the cell state at the current time step;

[0015] Output o after morphological enhancement by long short-term memory module t It is expressed as:

[0016] o t =σ(W o ·[h t-1 ,θ t ]+b o

[0017] h t =o t **tanh(C t )

[0018] In the formula, o t Represents the information to be output, C t represents the updated cell state, h t Represents the output result of the current sequence model;

[0019] Step 4: Set up the learning process of the long short-term memory autoencoder model:

[0020] Step 4.1: Set the loss function of the model training to the mean square error function, and calculate the point-by-point error of the sample pairs based on the mean square error function; the mean square error function is:

[0021]

[0022] In the formula, x i represents the pure hemodynamic response, x ri represents the near-infrared signal after model reconstruction, and n represents the sampling point size of the sample;

[0023] Step 4.2: Set the batch size of the model training to 512, the number of training rounds to 100, and the learning rate to 0.0001;

[0024] Step 5: Use the leave-one-out method for validation, train the model by simulating the data of all subjects except one, and test the model with the removed subject; repeat the above steps until all subjects are used for testing;

[0025] Step 6, synthesizing the hemodynamic response in the original near-infrared signal by introducing a signal change of 1% of the 690nm signal relative to the baseline and a signal change of 2% of the 830nm signal relative to the baseline, and adding the synthesized hemodynamic response to the real data containing motion artifacts collected in step 1;

[0026] Step 7, the real data with added synthetic hemodynamic response are imported into Homer2 software, the original real data are converted into optical density changes, band-pass processed to reduce low-frequency drift and high-frequency noise, and finally block averaged by block average function to evaluate the hemodynamic response;

[0027] Step 8: Introduce mean square error, signal-to-noise ratio, root mean square ratio, and Pearson correlation coefficient to calculate the recovery result of the hemodynamic response in step 7 to measure the ability of the long short-term memory autoencoder model to remove motion artifacts.

[0028] Furthermore, in step 3, when constructing the downsampling module, a one-dimensional convolutional layer is applied to the local feature mining of the original near-infrared signal, and a maximum pooling layer is added in each block to gradually downsample the near-infrared signal in the time domain to obtain deeper features; the feature vector filtered by the downsampling layer can be expressed as θ = (θ1, θ2, ..., θ N ), the long short-term memory module is used to measure the temporal correlation between individual samples, and the result is applied to the morphological features for feature enhancement. The feature representation process can be described as follows by capturing the temporal dynamic characteristics of the near-infrared signal:

[0029] h t ,c t =LSTM(h t-1 , c t-1 ,θ t )1 <t<N

[0030] Where h, c are the hidden layer state and unit state of the long short-term memory module; N is the total number of samples, θ t Represents the feature vector of the tth sample.

[0031] Furthermore, in step 3, when constructing the upsampling module, the multi-dimensional features after morphological feature extraction by the downsampling module and feature enhancement by the long short-term memory module are up-sampled, and finally the clean hemodynamic response after reconstructed by the denoising network is output at the terminal output layer.

[0032] Furthermore, in step 3, the downsampled features are concatenated with the upsampled features of each layer, which can prevent the information loss of the near-infrared signal during the upsampling process and retain more detailed features.

[0033] The present invention has the following characteristics and beneficial effects: Different from the motion artifact removal method of traditional signal processing which is overly dependent on professional knowledge and the optimal selection of model parameters of brain regions, the present invention uses an autoencoder model based on long short-term memory for motion artifact removal of near-infrared signals. This method can extract comprehensive features and information from the nonlinear and non-stationary original near-infrared signals, thereby solving the uncertain relationship between the original noisy signal and the pure signal, and the optimal denoising parameters are learned during the denoising process, thereby realizing fully automatic removal of motion artifacts. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0035] Figure 1 It is a flow chart of a method for removing artifacts of an autoencoder based on long short-term memory according to an embodiment of the present invention;

[0036] Figure 2 This is a structural diagram of the long short-term memory autoencoder model in an embodiment of the present invention. DETAILED DESCRIPTION

[0037] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0038] In order to fill the deficiency of motion artifact removal methods in traditional signal processing that are overly dependent on professional knowledge and the optimal selection of model parameters of brain regions, the present invention proposes a method for functional near-infrared artifact removal based on long short-term memory autoencoders. This method reduces motion artifacts by training a neural network to reconstruct the hemodynamic response coupled with neuronal activity. It first uses a deep neural network to denoise the near-infrared signal. In the training stage, each layer in the model is regarded as a filter to learn the core features output from the previous layer, and to input the filtered near-infrared waveform features to the next layer. The features extracted by the network can distinguish between real near-infrared (non-artifact) and artifacts. Then, after multiple layers of filtering, these features are used in the output layer to reconstruct artifact-free near-infrared signals. The artifact-containing near-infrared signal and the clean near-infrared signal output by the output layer are calculated point by point through the loss function to make the reconstructed near-infrared signal as consistent as possible with the pure near-infrared signal. The model reaches the optimal level through multiple training. Finally, in the testing stage, the trained model directly operates on the original near-infrared signal and generates a predicted artifact-free near-infrared signal, such as Figure 1 As shown, the specific steps include:

[0039] Step 1. Collecting action data of multiple subjects: multiple subjects read aloud, nod their heads up and down, nod their heads to the side, twist their upper body to the right, twist their upper body to the left, shake their heads left and right quickly, and raise their eyebrows to generate data of motion artifacts.

[0040] Step 2: Split the dataset into training set, validation set, and test set in a ratio of 8:1:1.

[0041] Step 3: Construct an autoencoder model based on long short-term memory. The denoising module of the autoencoder model consists of a downsampling module, a long short-term memory module, and an upsampling module. The construction includes the following steps:

[0042] Step 3.1: Construct a downsampling module. The present invention applies a one-dimensional convolutional layer to the local feature mining of the original near-infrared signal. A maximum pooling layer is added in each block to gradually downsample the near-infrared signal in the time domain to obtain deeper features. The feature vector filtered by the downsampling layer can be expressed as θ = (θ1, θ2, ..., θ N ).

[0043] Step 3.2: Construct a long short-term memory module. The long short-term memory module is used to measure the temporal correlation between individual samples and apply the results to the morphological features for feature enhancement. The long short-term memory module captures the temporal dynamic characteristics of the near-infrared signal to enhance the feature representation process, which can be described as:

[0044] h t , c t =LSTM(ht-1 , c t-1 ,θ t )1 <t<N (1)

[0045] Where h, c are the hidden layer state and cell state of the long short-term memory module, N is the total number of samples, θ t The feature vector representing the tth sample;

[0046] The calculation process of the long short-term memory module consists of the following steps:

[0047] f t =σ(W f ·[h t-1 ,θ t ]+b f ) (2)

[0048] i t =σ(W i ·[h t-1 ,θ t ]+b i ) (3)

[0049]

[0050] In the formula, f t ,i t , Represents the forget gate, input gate and represents the new cell state created using tanh. W represents the weight matrix, b represents the bias parameter, and b f 、b i 、b c Represents the bias parameters of the forget gate, input gate and cell state respectively. σ represents the sigmoid activation function, and the output value is between 0 and 1. tanh represents the hyperbolic tangent activation function, and the output value is between -1 and 1. h t-1 represents the hidden state of the previous time step, C t-1 represents the cell state at the previous time step, C t Represents the cell state at the current time step.

[0051] Output o after morphological enhancement by long short-term memory module t It is expressed as:

[0052] o t =σ(W o ·[h t-1 ,θ t ]+b o ) (6)

[0053] h t =o t *tanh(Ct ) (7)

[0054] In the formula, o t represents the output result of the feature vector enhancement of the tth sample by the current module, h t Represents the hidden state at the current time step.

[0055] Step 3.3, construct an upsampling module, upsample the multi-dimensional features after morphological feature extraction by the downsampling module and feature enhancement by the long short-term memory module, and finally output the clean hemodynamic response after reconstructing the denoising network at the terminal output layer.

[0056] Step 3.4: Concatenating the downsampled features with the upsampled features of each layer can prevent the loss of near-infrared signal information during the upsampling process and retain more detailed features.

[0057] Step 4: Set up the learning process of the long short-term memory autoencoder model. Specifically:

[0058] Step 4.1. Set the loss function of model training to mean square error function:

[0059]

[0060] In the formula, x i represents the pure hemodynamic response, x ri represents the near-infrared signal after model reconstruction, n represents the sampling point size of the sample, and the mean square error function calculates the error of the sample pair point by point.

[0061] Step 4.2: Set the batch size of the model training to 512, the number of training rounds to 100, and the learning rate to 0.0001.

[0062] Step 5: Use the leave-one-out method for validation. Train the model by simulating the data of all subjects except one, test the model with the removed subject, and repeat the above steps until all subjects are used for testing.

[0063] like Figure 2As shown, the long short-term memory autoencoder model constructed by the present invention includes the following steps when working: 1) extracting morphological features from the original near-infrared signal through a downsampling module; 2) enhancing the morphological features of the original near-infrared signal after the morphological features are extracted by the downsampling module by measuring the time correlation between single samples through a long short-term memory module; 3) the original near-infrared signal after the morphological features are enhanced by the long short-term memory module is restored and reconstructed through an upsampling module, and in the process of upsampling, the outputs of each layer in the downsampling and upsampling modules are spliced ​​to prevent the loss of information of the near-infrared signal during the upsampling process, thereby retaining more detailed features; 4) finally, the upsampled morphological features are aggregated in the output layer to generate a reconstructed pure near-infrared signal.

[0064] Step 6: Synthesize the hemodynamic response in the original near-infrared signal by introducing a signal change of 1% of the 690nm signal relative to the baseline and a signal change of 2% of the 830nm signal relative to the baseline, and add the synthesized hemodynamic response to the real data containing motion artifacts collected in step 1.

[0065] Step 7: Import the real data with synthetic hemodynamic response added into Homer2 software, convert the original real data into optical density changes, perform bandpass processing to reduce low-frequency drift and high-frequency noise, and finally perform block averaging through the block averaging function to evaluate the hemodynamic response.

[0066] Step 8: Synthesize simulation data:

[0067] The simulated near-infrared signal can be described as y(t):

[0068] y(t)=z(t)+r(t))+ε(t) (9)

[0069] Where z(t) simulates the hemodynamic response, r(t) simulates the near-infrared motion artifact, and ε(t) simulates the resting near-infrared signal.

[0070] The simulated hemodynamic response z(t) is generated by convolving the task stimulus function u(t) with the canonical hemodynamic response function h(t), which can be described as:

[0071] z(t)=u(t)*h(t) (10)

[0072] The standard hemodynamic response h(t) is simulated by a gamma function, where the response function amplitude is 54 μ M·mm. In this invention, we set the amplitude to 40 ～ 80 μ We select random values ​​between M·mm distributions so that our model can learn between samples with different parameters.

[0073] The task stimulus function u(t) is expressed as:

[0074]

[0075] In the formula, B represents the boxcal function, b is the duration of stimulation, t1 represents the duration of rest, t2 represents the time shift factor of stimulation, i(b+t1) represents the stimulation phase, t s Indicates the time point when the spike occurs.

[0076] The hemodynamic response stimulation interval is 70s, and multiple stimulations can be provided during the 6-minute recording period. The resting-state data generated by the AR model from the real resting data, the simulated motion artifact ε(t) includes two parts: baseline offset and spike θ(t), θ(t) can be described as:

[0077]

[0078] Where A represents the amplitude of the spike artifact, t s represents the time point when the spike occurs, b represents the scale parameter, and e represents the Laplace distribution function. (12) can be rewritten as

[0079] Baseline shift artifacts were modeled as random positive or negative variations in the fNIRS analog signal, ranging between −20 μM·mm and 20 μM·mm.

[0080] Step 9: Use mean square error, signal-to-noise ratio, root mean square ratio, and Pearson correlation coefficient to calculate the recovery results of the hemodynamic response of the real data set in step 7 and the simulated data set in step 7 to measure the ability of the long short-term memory autoencoder model to remove motion artifacts. Among them:

[0081] Mean Square Error:

[0082]

[0083] In the formula, HRF represents the standard hemodynamic response, and HRF′ represents the hemodynamic response with motion artifacts. Here, MSE represents the error between the true hemodynamic response and the denoised hemodynamic response. The smaller the MSE, the better the denoising result.

[0084] Signal-to-Noise Ratio:

[0085]

[0086] In the formula, ΔSNR is an indicator of the signal-to-noise ratio. The larger the ΔSNR is, the better the denoising result is.

[0087] Percentage ratio:

[0088]

[0089] The percentage ratio indicates the degree of matching between two signals. The smaller the PDR result, the higher the signal matching degree, which shows that the motion artifact content in the signal is lower.

[0090] Pearson correlation coefficient:

[0091]

[0092] In the formula, R 2 Represents the similarity between the real signal and the processed signal, R 2 The larger the value, the better the denoising effect.

[0093] The results are shown in Tables 1 and 2. The proposed long short-term memory autoencoder method for implementing functional near-infrared artifact removal outperforms the traditional method in various indicators on both simulated and real datasets, showing reasonable motion artifact removal capabilities.

[0094] Table 1: Mean square error (MSE), Pearson correlation coefficient (R) of different motion artifact correction algorithms on the simulated data set 2 ), signal-to-noise ratio (ΔSNR), and percentage-to-noise ratio (PDR) values

[0095]

[0096] Table 2: Mean square error (MSE), Pearson correlation coefficient (R) of different motion artifact correction algorithms on real data sets 2 ), signal-to-noise ratio (ΔSNR), and percentage-to-noise ratio (PDR) values

[0097]

[0098] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. The above embodiments and descriptions are only preferred examples of the present invention and are not intended to limit the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for implementing functional near-infrared artifact removal based on long short-term memory autoencoder, characterized in that: The steps include: Step 1: Collecting the execution action data of multiple subjects; Step 2: Split the data set into training set, validation set, and test set in a ratio of 8:1:1; Step 3: construct an autoencoder model based on long short-term memory, wherein the denoising module of the autoencoder model consists of a downsampling module, a long short-term memory module and an upsampling module; Step 4: Set up the learning process of the long short-term memory autoencoder model; Step 5: Use the leave-one-out method for validation, train the model by simulating the data of all subjects except one, and test the model with the removed subject; repeat the above steps until all subjects are used for testing; Step 6, synthesizing a hemodynamic response in the original near-infrared signal by introducing a signal change, and adding the synthesized hemodynamic response to the real data containing motion artifacts collected in step 1; Step 7, the real data with added synthetic hemodynamic response are imported into Homer2 software, the original real data are converted into optical density changes, band-pass processed to reduce low-frequency drift and high-frequency noise, and finally block averaged by block average function to evaluate the hemodynamic response; Step 8: Introduce mean square error, signal-to-noise ratio, root mean square ratio, and Pearson correlation coefficient to calculate the recovery result of the hemodynamic response in step 7 to measure the ability of the long short-term memory autoencoder model to remove motion artifacts.

2. The method for implementing functional near-infrared artifact removal based on long short-term memory autoencoder according to claim 1, characterized in that: The execution action data in step 1 includes data of reading aloud, nodding up and down, nodding to the side, twisting the upper body to the right, twisting the upper body to the left, shaking the head quickly left and right, and raising eyebrows to generate motion artifacts.

3. The method for implementing functional near-infrared artifact removal based on long short-term memory autoencoder according to claim 1, characterized in that: In step 3, when constructing the downsampling module, a one-dimensional convolution layer is applied to the local feature mining of the original near-infrared signal, and a maximum pooling layer is added in each block to gradually downsample the near-infrared signal in the time domain to obtain deeper features.

4. The method for implementing functional near-infrared artifact removal based on long short-term memory autoencoder according to claim 1, characterized in that: In step 3, the calculation process of the long short-term memory module consists of the following steps: f t =σ(W f ·[h t-1 ,the t ]+b f ) I t =σ(W i ·[h t-1 ,the t ]+b i ) In the formula, f t ,i t , represents the forget gate, the input gate and represents the new cell state created using tanh, W represents the weight matrix, b f 、b i 、b c They represent the bias parameters of the forget gate, input gate and cell state respectively; σ represents the sigmoid activation function, and the output value is between 0 and 1; tanh represents the hyperbolic tangent activation function, and the output value is between -1 and 1; h t-1 represents the hidden state of the previous time step, C t-1 represents the cell state at the previous time step, C t Represents the cell state at the current time step; Output o after morphological enhancement by long short-term memory module t It is expressed as: the t =σ(W o ·[h t-1 ,the t ]+b o h t =o t *tanh(C t ) In the formula, o t Represents the information to be output, C t represents the cell state after update, h t Represents the output result of the current sequence model.

5. The method for implementing functional near-infrared artifact removal based on long short-term memory autoencoder according to claim 1, characterized in that: In step 3, the feature vector filtered by the downsampling layer can be expressed as θ=(θ1, θ2, ..., θ N ), the long short-term memory module is used to measure the temporal correlation between individual samples, and the result is applied to the morphological features for feature enhancement. The feature representation process can be described as follows by capturing the temporal dynamic characteristics of the near-infrared signal: h t ,c t =LSTM(h t-1 ,c t-1 ,θ t ) 1<t<N Where h and c are the hidden layer state and unit state of the long short-term memory module.

6. The method for implementing functional near-infrared artifact removal based on long short-term memory autoencoder according to claim 1, characterized in that: In step 3, when constructing the upsampling module, the multi-dimensional features after morphological feature extraction by the downsampling module and feature enhancement by the long short-term memory module are up-sampled, and finally the clean hemodynamic response after reconstructed by the denoising network is output at the terminal output layer.

7. The method for implementing functional near-infrared artifact removal based on long short-term memory autoencoder according to claim 1, characterized in that: In step 3, the downsampled features are concatenated with the upsampled features of each layer, which can prevent the information loss of the near-infrared signal during the upsampling process and retain more detailed features.

8. The method for implementing functional near-infrared artifact removal based on long short-term memory autoencoder according to claim 1, characterized in that: The step 4 comprises the following steps: Step 4.1, set the loss function of the model training to the mean square error function, and calculate the point-by-point error of the sample pairs based on the mean square error function; Step 4.2: Set the batch size of the model training to 512, the number of training rounds to 100, and the learning rate to 0.0001.

9. The method for implementing functional near-infrared artifact removal based on long short-term memory autoencoder according to claim 8, characterized in that: The mean square error function in step 4.1 is: In the formula, x i represents the pure hemodynamic response, x ri represents the near-infrared signal after model reconstruction, and n represents the sampling point size of the sample.

10. The method for implementing functional near-infrared artifact removal based on long short-term memory autoencoder according to claim 8, characterized in that: In step 6, a hemodynamic response is synthesized in the original near-infrared signal by introducing a signal change of 1% of the 690nm signal relative to the baseline and a signal change of 2% of the 830nm signal relative to the baseline, and the synthesized hemodynamic response is added to the real data containing motion artifacts collected in step 1.

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