# Diffuse Optical Tomography Using Bayesian Filtering in the Human Brain
## 1 Introduction  
Functional brain imaging has provided substantial information regarding how dynamic neural processes are distributed in space and time. Some imaging modalities to study brain function use functional magnetic resonance imaging (fMRI) and, although these measurements can cover the entire brain, they require costly infrastructure. Technical limitations in fMRI devices, such as a fixed scanner, contraindication with metal implants, scanner noise, and stress associated with fear, are avoided or reduced using optical imaging devices. In addition, optical imaging techniques, such as functional near infrared spectroscopy (fNIRS), can measure changes in oxyhemoglobin (HbO) and deoxyhemoglobin (HbR) at a much higher sampling rate than fMRI devices. Therefore, contrary to positron emission tomography (PET) [1] or X-ray computed tomography [2], optical imaging does not require a contrast agent, which, hence, avoids issues, such as limited doses for infants or anaphylactic reactions. Moreover, optical imaging techniques are low-cost when compared to other neuroimaging techniques, such as fMRI or magnetoencephalography (MEG). These circumstances have potentiated the optical imaging techniques development in recent years in research, diagnosis, and prognostic studies.  
The first biomedical application of NIR light in the human tissue was published in 1977 by [PERSON] [3], showing blood oxygenation measurements while using NIR light of approx. 700-1300 nm wavelength. This is known as the optical window, because NIR light at this wavelength can pass through the tissue, to a depth of around 3-4 cm [4]. Because of the presence of the natural chromophores in the tissue (HbO & HbR) that absorb NIR light, both are used as cerebral activation markers [5].  
NIR light is applied on the subject head through LEDs or optical fibers, which are combined as a source-detector pair, recording the changes in the optical density generated by changes in the optical properties in each tissue layer of the human head. Diffuse optical tomography (DOT) devices measurehemodynamic changes that are correlated with neural activity, caused by dynamics in blood volume, blood flow and blood oxygenation. Certain physiological signals, such as heart rate or ventilation rate, are involved in systemic blood oxygen and cerebral hemodynamics and, hence, influence the scalp layer [6]. During functional DOT neuroimaging experiments, these physiological signals create background noise. This noise is stronger than those in anatomical regions and mixed with absorbed signals from the cortex, thereby generating short-term variability that involves spatial and temporal changes throughout the brain and scalp [7]. Some researchers have devised methods to filter out the background physiological noise from the signals generated by neural activation. The most common methods are linear filtering, such as the application of band pass filter [8], low pass filter [9], high pass filter [10], adaptive filter [11], or principal component analysis [12], depending on the task or study area. A common problem during the processing of DOT data, which generally occurs during signal filtering, is that the judgment of the researcher might lead to an error in the cutoff frequencies selected. Because of this, a more robust and independent procedure is necessary. Using the Bayesian algorithm application as a filter method on the raw DOT data will allow for an independent procedure, without the influence of the researcher, paradigm, or cerebral area for study, which is more accurate than the linear methods used so far. Here, we describe a Bayesian method to model physiological data and separate it from the neural response, which avoids the common filtering controversies during the DOT data processing.