• Adaptive filtering
• Autocorrelated Noise
• BOLD signal
• Functional Connectivity
• Nonstationarity Test
• Principal Component Analysis
• Resting State
• RV Coefficient
• Singular Spectrum Analysis

Functional Magnetic Resonance Imaging (fMRI) is used to investigate brain functional connectivity at rest after filtering out non-neuronal components related to cardiac and respiratory processes and to the instrumental noise of MRI scanner. These components are generally removed at their fundamental frequencies through band-pass filtering of the Blood-Oxygen-Level-Dependent (BOLD) signal (low-frequency band – LFB: 0.01–0.10 Hz) while General Linear Model (GLM) is usually employed to suppress slow variations of physiological noise in the LFB, using a signal template derived from non-neuronal regions (e.g. brain ventricles). However, these sources of noise exhibit a non-stationary nature due to the intrinsic time variability of physiological activities or to the nonlinear characteristics of MRI scanner drifts: at present, the standard procedure (band-pass filtering and GLM) does not take into account these noise properties in the processing of BOLD signal.
This thesis proposes the joint usage of two methods (Singular Spectrum Analysis – SSA – and adaptive filtering) that takes advantage of their statistical and time flexibility features, respectively. Indeed SSA is a nonparametric technique capable of extracting amplitude and phase modulated components against a null hypothesis of autocorrelated noise, while the adaptive filter removes the noise correlated to a reference signal, exploiting its non-stationary properties.
The novel procedure (SSA and adaptive filtering) was applied to eight resting state recordings and compared to the standard procedure. The functional connectivity between homologous contralateral regions was then estimated in the LFB using a multivariate correlation index (the RV coefficient) and assessed on preselected grey (GM) and white matter (WM) regions of interest (ROIs). A corrected version of the RV coefficient for the number of voxels was developed and used to compare the functional connectivity estimates obtained by the standard procedure (using all available voxels) and from the novel procedure based on the voxel time courses with significant SSA components in the LFB (active voxels).
The adaptive filtering showed a greater reduction of noise compared to GLM (average signal variance decrease in all ROIs: −43.9% vs. −10.1%), using a non-stationary noise template obtained from brain ventricles signals in the LFB. The functional connectivity quantified by the RV coefficient and estimated on the active voxels identified by SSA showed a higher contrast between GM and WM regions with respect to the standard procedure (35% vs. 28%).
These results suggest that SSA and adaptive filtering may be a feasible procedure for properly removing the physiological noise in the LFB of BOLD signal and for highlighting resting state functional networks.