## 1 Introduction  
Functional near-infrared spectroscopy (fNIRS) [1] has gained interest in recent years as a noninvasive neuroimaging technique to investigate cortical activity, along with techniques such as functional magnetic resonance imaging (fMRI) and electroencephalography. fNIRS is thought to indirectly reflect neural activity through neurovascular coupling by detecting changes in light scattering and absorption within the tissue caused by changes in the concentration of oxyhemoglobin (\(\Delta\)HbO) and deoxyhemoglobin (\(\Delta\)Hb). Besides fNIRS' many practical advantages such as portability, compatibility with other techniques, no requirements for a special environment, and no restriction on the subject population, its technical advantages lie in its temporal resolution (~25 to 100 Hz) of hemoglobin concentration measurements (practically only restricted by the hemodynamic response function itself) and the ability to distinguish between both chromophores, oxyhemoglobin, and deoxyhemoglobin. However, major challenges include (1) relatively poor spatial resolution (1 to 3 cm\({}^{3}\)) caused by the scattering of light in tissue and the geometry of the light sources and detectors on the surface of the head which can only be alleviated with a dense cluster of overlapping channels; (2) the limited penetration depth (1 cm of cerebral cortex [2]); and (3) contamination from noise sources including instrumental noise, experimental noise, and physiological artifacts [3]. Hence, one of the greatest challenges in fNIRS research is the accurate delineation of the masking effects of the noise sources from the desired \"neuronal\" brain signal. Functional magnetic resonance imaging (fMRI) has long been the gold standard of non-invasive brain imaging due to its high spatial resolution over the whole head. Since the development of multiband/simultaneous multislice (SMS) acquisition [4; 5], simultaneous high spatial (1-2 mm isotropic) and temporal resolution (\(\sim\)0.7 s) are now possible. fMRI exploits the effect of blood oxygenation on the magnetic properties of hemoglobin, just as fNIRS uses the effect on its optical properties, to make inferences about underlying neuronal activity changes in the brain; however, it lacks the ability to separately quantify oxyhemoglobin and deoxyhemoglobin changes and still struggles to approach the temporal resolution of fNIRS (resulting in the poor quantification of cardiac effects). Due to the complementary strengths of fNIRS and fMRI in temporal and spatial resolution, respectively, multimodal studies often utilize fNIRS and fMRI simultaneously which has shed light on various aspects of each method [6]. Since fNIRS optodes are directly positioned on the scalp of the participant, fNIRS is in general considered less sensitive to head motion artifacts than fMRI, which depend on stationary sensors. However, motion artifacts are still a problem for fNIRS because the coupling between the optodes and the skin is altered when the optode is displaced. This introduces a strong external noise which produces spurious differences that can mask patterns arising from neural activity. Therefore, despite the relative insensitivity of fNIRS to head motion, it is still necessary to apply processing strategies that eliminate these artifacts. A wide variety of motion artifact elimination techniques have been proposed ([7; 8]). These techniques can be categorized based on the temporal or spatial characteristics of the signal and methods that use external signals for movement artifact removal by adaptive filtering. The motion-correction algorithms, which have been developed for fNIRS data, suffer from different drawbacks. For example, some of the wavelet-based methods (e.g., [9; 10]) are well equipped to remove motion spikes; however, exacerbate baseline shifts artifacts. Especially, methods relying on global temporal characteristics (such as PCA-based methods) require a certain number of channels to perform accurate delineation between the noise and signal, as do spatially based methods.