## 1 Introduction
Other methods such as the Movement Artifact Reduction Algorithm (MARA) [11] rely on several parameters that must be supplied by the user to detect artifacts, which is usually disadvantageous. AMARA (acceleration-based movement artifact reduction algorithm) [12] is one of those methods but also one of the most promising automatic motion correction methods for fNIRS analysis. The method identifies motion artifacts using an accelerometer and combines two previous motion detection and removal methods, MARA [11] and ABAMAR [13]. It has been tested on long fNIRS sleep study acquisitions (\(\sim\)8 h) and compares favorably to both MARA and ABAMAR. Motion displacement parameters can be easily acquired from fMRI with FSL MCFLIRT [14; 15] or AFNI 3 dvolReg [16; 17], two standard pre-processing programs for fMRI data. The second derivative of the motion time courses of fMRI can therefore be used to determine the acceleration-based movement in fNIRS. However, here, the relatively low temporal resolution of fMRI is problematic; it would be highly advantageous if the acceleration time courses could be derived at the same, much higher temporal resolution of the fNIRS data. Here, we propose a new way to increase the temporal resolution of acceleration data derived from the fMRI motion measurements. We do so by adapting and expanding a method we developed for increasing the time resolution of motion data in fMRI by taking into account the slice acquisition time and reconstructing high-resolution motion time courses [18]. Similar techniques have been proposed using slice-wise motion correction [19] and have been applied for real-time motion correction [20; 21] with slice-to-volume registration in which guided breath-hold at 0.34 Hz could be observed in one subject [20]. These techniques, such as the one by [PERSON] et al. [20], rely on advanced iterative algorithms. Our technique was developed to reconstruct respiration, as a complement to our cardiac waveform reconstruction method [22] using slice sorted averaging and a deep learning reconstruction filter. Although a deep learning approach was highly successful in our previous work and our current method might benefit from that, in this situation, unlike the cardiac waveform generation, we did not have ground truth high-frequency motion data. However, this method performs very well, reconstructing respiration, cardiac, and high-resolution motion without requiring any advanced modeling and instead by simply reorganizing slices according to their acquisition times [18]. Machine learning is especially useful for extrapolating information which is not directly available in a particular dataset by automatically finding patterns and interrelationships within datasets in the absence of a model, and then applying this to fill in missing information. However, when there are known characteristics of the system (in this case, that the head is a rigid structure and motion of one part of the head means that the rest of the head undergoes similar motion), it is always preferable to incorporate this information to minimize the degree to which the other parts of the system need to \"learn\" these relationships. Here, we incorporate this information into deriving a better motion time course, so that AMARA is more firmly within the regime that it was developed to handle (that certain types of motion cause transients in fNIRS data that can be removed). In the following, we show how this method can be used in conjunction with automatic motion correction methods in fNIRS such as AMARA in order to enhance signal detection.