# Improved Motion Artifact Correction in fNIRS Data by Combining Wavelet and Correlation-Based Signal Improvement

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Motion Artifact Correction Methods

_{0}and Y

_{0}generated by HbO and HbR concentration changes in the brain, (2) movement-related noise causing similar effects F on HbO and HbR but with different scaling captured by a positive constant factor α, and (3) instrument noise. The observed HbO and HbR measurements X and Y can then be written as

_{0}and Y

_{0}are perfectly negatively correlated, we can express one as a negatively scaled version of the other X

_{0}= −βY

_{0}with β as the scaling factor. Based on empirical observations, the authors of [20] argue that the scaling α of the movement-induced noise is similar to the scaling β of the true HbO/HbR signals, i.e., α = β. With these assumptions, they derive the following equations:

#### 2.2. Experimental Procedure and fNIRS Data Recording

#### 2.2.1. Participants

#### 2.2.2. Experimental Setup and Procedure

#### 2.2.3. fNIRS and IMU Data Recording and Processing

#### 2.2.4. Data Processing and Movement Correction

## 3. Quality Metrics for Comparison among MA Correction Algorithms

- (1)
- Pearson’s correlation coefficient R was calculated between the averaged HRF of the reference signal $HRF$ (NHM) and $\widehat{HRF}$ of the movement-contaminated signals (SHM and LHM). Pearson correlation measures the similarity of the shapes of two signals and is scaled between −1 and 1.

- (2)
- Rooted Mean Square Error (RMSE) measures the unscaled average deviation between two signal time series. It was calculated with the following equation:$$RMSE=\sqrt{\frac{{\sum}_{i=1}^{N}{(HRF\left(i\right)-\widehat{HRF}\left(i\right))}^{2}}{N}}$$

- (3)
- Mean Absolute Percentage Error (MAPE) measures the deviation in relation to the momentary strength of the reference signal. It was obtained with the formula:

- (4)
- The area under the curve difference (ΔAUC) is a global measure that compares the overall deviation from the baseline of two curves. It was obtained with the formula:

## 4. Movement Analysis

## 5. Results

#### 5.1. Movement Analysis

#### 5.2. fNIRS Movement Artifacts

#### 5.3. Comparison of Movement Correction Methods

^{−5}- for HbO and 1.2 × 10

^{−5}for HbR; LHM: 2.4 × 10

^{−5}for HbO and 1.5 × 10

^{−5}for HbR). In decibels, this corresponds to a noise reduction of −12.2 dB for HbO and −10.6 dB for HbR with SHM and with LHM −15.1 dB for HbO and −13.9 dB for HbR. For larger head movements, the RMSE is comparable between RLOESS and WCBSI, but for smaller movements there is still a clear improvement in WCBSI over RLOESS (HbO: 53%, HbR: 17% improvement). Note that the generally lower RMSE for the HbR signals is due to the generally lower signal variation compared to HbO.

^{−4}for HbO and 1.1 × 10

^{−4}for HbR; LHM: 1.0 × 10

^{−4}for HbO and 1.4 × 10

^{−4}for HbR). In decibels, this corresponds to a noise reduction of −9.6 dB for HbO and −14.9 dB with SHM and with LHM −21.4 dB for HbO and −13.7 dB for HbR. Note that for HbR, the ΔAUC performance is very similar between movement conditions. For the combination SHM and HbO, WCBSI is still in the middle field after wavelet, CBSI, and RLOESS. For all other combinations of movement and fNIRS signal, WCBSI provides the best ΔAUC measures.

## 6. Discussion

## 7. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The flow of data for all MA correction techniques tested here. The rounded rectangles indicate the processing steps applied to the data. The data flow of each technique is indicated by color-coded arrows: black for uncorrected data, blue for spline, cyan for spline SG, yellow for RLOESS, gray for wavelet, brown for CBSI, green for PCA, purple for tPCA, and red for WCBSI correction. The red dashed box indicates how processes are combined in the WCBSI correction. All parameters used in the respective MA correction algorithms are listed in Table 1.

**Figure 2.**(

**a**) Optode placement. We recorded using eight optodes placed according to the 10/20 system in positions approximately located over the hand area of the primary motor cortices. The two detectors placed at C3 and C4 are marked in blue, and the sources located at FC3, FC4, CP3, CP4, C1, C2, C5, and C5 are marked in red. The black lines approximate the channels. The accelerometer was located in the FCz position and is indicated by a black box. (

**b**) The participant is seated in front of the monitor with his/her hands on the table. Arrows indicate the approximate directions of the head movements.

**Figure 3.**The experimental procedure and sequence of the tasks. The participants first performed hand tapping without head movements for 10 s (NHM), then, after a 20 s rest period, hand tapping with small head movements (SHM) for 10 s, and, after a 20 s rest period, hand tapping with large head movements (LHM) for 10 s, followed by a 20 s rest period. This sequence was repeated 25 times. A baseline was recorded at the beginning and the end of the experiment.

**Figure 4.**Mean head acceleration over participants for all three movement conditions (NHM, SHM, LHM). Error bars indicate standard error across participants.

**Figure 5.**(

**a**) An example raw time course of optical density signals of one participant (red: HbO, blue: HbR). The small insets exemplify different types of MA (baseline shifts, spikes with high amplitude and fast dynamics, and slow drifts with lower amplitude and slower dynamics) at a finer temporal scale. (

**b**) Corresponding average uncorrected epochs of the raw concentration change of HbO/HbR for the three movement conditions. Different levels of movement artifacts distort the tapping related response to different extents, even after averaging. Colors codes conditions: red for HbO in NHM epochs, blue for HbR in NHM, black for HbO in LHM epochs, green for HbR in LHM, purple for HbO in SHM, and cyan for HbR in SHM. Error bands indicate standard error across trials.

**Figure 6.**Average Pearson correlations of the MA corrected HbO and HbR signals with the reference signals. These are shown in (

**a**) for the SHM responses and in (

**b**) for the LHM responses. The correlations were calculated individually for each participant and then averaged. Correction types are uncorrected, principal component analysis (PCA), spline interpolation, spline interpolation plus Savitzky–Golay filtering (splineSG), correlation-based signal improvement (CBSI), wavelet transform, targeted principal component analysis (tPCA), robust locally estimated scatter plot smoothing (RLOESS), and our new combination of wavelet and CBSI correction (WCBSI). Error bars indicate standard error across participants.

**Figure 7.**Average rooted mean square error (RMSE) between the MA corrected HbO and HbR signals and their respective reference signal. This is shown in (

**a**) for the SHM responses and in (

**b**) for the LHM responses. The RMSEs were calculated individually for each participant and then averaged. Error bars indicate standard error across participants.

**Figure 8.**Mean absolute percentage error (MAPE) between the MA corrected HbO and HbR signals and their respective reference signals. This is shown in (

**a**) for the SHM responses and in (

**b**) for the LHM responses. The MAPEs were calculated individually for each participant and then averaged. Error bars indicate standard error across participants.

**Figure 9.**Mean difference between areas under curve (ΔAUC) of the MA corrected HbO and HbR signals and their respective reference signals. This is shown in (

**a**) for the SHM responses and in (

**b**) for the LHM responses. The ΔAUCs were calculated individually for each participant and then averaged. Error bars indicate standard error across participants.

**Figure 10.**The log worth of the different MA correction methods obtained by fitting a Plackett–Luce model to the ranking data. Higher values indicate better performance of the correction algorithm. WCBSI has the highest worth and “uncorrected” the lowest. All other correction algorithms have similar worths varying around the mean. All worths are referenced to “uncorrected”, for which the mean was set to zero. Error bars indicate standard errors of the mean.

Name | Function | Parameters and Values |
---|---|---|

Channel rejection | hmrR_PruneChannels | dRange (1 × 10^{−4}–1 × 10^{7}), SNRthresh = 1, Sdrange = (0.0–45.0) |

Motion detection | HmrMotionArtifactByChannel | tMotion = 0.5 Sec, tMask = 1.0 Sec, SDEVThresh = 20, AMPthresh = (0.05–0.5) |

PCA | hmrR_PCAFilter | nSV = (0.96 ± 0.02) |

tPCA | hmrR_MotionCorrectPCArecurse | tMotion = 0.5 Sec, tMask = 1.0 Sec, SDEVThresh = 20, AMPthresh = (0.1–0.5), nSV = 0.97, maxlter = 5 |

Spline | hmrR_MotionCorrectSpline | p = 0.99 |

SplineSG | hmrR_MotionCorrectionSplineSG | p = 0.99, FrameSize_Sec = 10 |

RLOEES | hmrR_MotionCorrectRLOEES | span = 0.02 |

Wavelet | hmrR_MotionCorrectWavelet | iqr = 1.5 |

CBSI | hmrR_MotionCorrectCBSI | On |

Band-pass filter | hmrR_BandpassFilt | hpf = 0.01 Hz, lpf = 0.1 Hz |

OD change | hmrR_OD2Conc | 1.0 1.0 1.0 |

Average | hmrR_BlockAvg | −2.0 Sec 20.0 Sec |

Method | Grand Mean Rank | Rank std |
---|---|---|

WCBSI | 1.25 | 0.77 |

RLOESS | 4.00 | 2.48 |

CBSI | 4.13 | 2.13 |

Wavelet | 4.25 | 2.27 |

SplineSG | 4.94 | 2.24 |

Spline | 5.44 | 1.46 |

tPCA | 5.63 | 1.59 |

PCA | 6.31 | 1.78 |

Uncorrected | 8.63 | 0.81 |

Method | Rank Grand Mean | Rank std |
---|---|---|

WCBSI | 1.25 | 0.77 |

Uncorrected | 8.63 | 0.81 |

Spline | 5.44 | 1.46 |

tPCA | 5.63 | 1.59 |

PCA | 6.31 | 1.78 |

CBSI | 4.13 | 2.13 |

SplineSG | 4.94 | 2.24 |

Wavelet | 4.25 | 2.27 |

RLOESS | 4.00 | 2.48 |

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**MDPI and ACS Style**

Al-Omairi, H.R.; Fudickar, S.; Hein, A.; Rieger, J.W.
Improved Motion Artifact Correction in fNIRS Data by Combining Wavelet and Correlation-Based Signal Improvement. *Sensors* **2023**, *23*, 3979.
https://doi.org/10.3390/s23083979

**AMA Style**

Al-Omairi HR, Fudickar S, Hein A, Rieger JW.
Improved Motion Artifact Correction in fNIRS Data by Combining Wavelet and Correlation-Based Signal Improvement. *Sensors*. 2023; 23(8):3979.
https://doi.org/10.3390/s23083979

**Chicago/Turabian Style**

Al-Omairi, Hayder R., Sebastian Fudickar, Andreas Hein, and Jochem W. Rieger.
2023. "Improved Motion Artifact Correction in fNIRS Data by Combining Wavelet and Correlation-Based Signal Improvement" *Sensors* 23, no. 8: 3979.
https://doi.org/10.3390/s23083979