Improvement in Recovery of Hemodynamic Responses by Extended Kalman Filter With Non-Linear State-Space Model and Short Separation Measurement

Objective: The purpose of this study is to describe the noise reduction in the hemodynamic responses, obtained by functional near-infrared spectroscopy (fNIRS), using the proposed extended Kalman filter (EKF) with a non-linear state-space model, aided by the short separation (SS) measurement. Methods: The authors used the simulated data by adding the synthetic hemodynamic response function (HRF) to the multi-distance four-channel fNIRS signals obtained during the resting state. EKF was used to estimate the non-linear state-space model designed based on the Balloon model. The SS channel was used as a regressor that is sensitive only to superficial noises. The whole segments were grouped by the existence of motion artifacts (MAs) to investigate the improvement by EKF compared to the linear Kalman filter (LKF) and adaptive filter (AF) in extracting neural-evoked hemodynamic. Results: Kalman-based approaches were better than AF in reducing noises. Using EKF, the averages of the decreased errors and increased correlation between the recovered and true HRF were 34% in oxy-hemoglobin and 62% in deoxy-hemoglobin concentrations in segments having MAs, compared with LKF. In the MA-free condition, EKF is more robust to the poor quality of signals in noise reduction than LKF. Conclusion: The proposed non-linear Kalman approach is better in noise reduction than AF and LKF especially in noisy deoxy-hemoglobin concentrations, and less affected by the conditions of measurements and contaminations by MAs. Significance: The proposed method can be used for reducing superficial noises and MAs from fNIRS signals as an upgraded alternative to existing AFs.