fMRI signal modeling using Laguerre polynomials
In order to construct spatial activation plots from functional magnetic resonance imaging (fMRI) data, a complex spatio-temporal modeling problem must be solved. A crucial part of this process is the estimation of the hemodynamic response (HR) function, an impulse response relating the stimulus signal to the measured noisy response. The estimation of the HR is complicated by the presence of low frequency colored noise. The standard approach to modeling the HR is to use simple parametric models, although FIR models have been used. We pursue a nonparametric approach using orthonormal causal Laguerre polynomials which have become popular in the system identification literature. It also happens that the shape of the basis elements is similar to that of a typical HR. We thus expect to achieve a compact and so bias reduced and low noise representation of the HR. This is not the case in FIR modeling, because a low FIR order is unable to cover the whole length of the HR over its region of support while a high FIR order results in overestimation of signal and underestimation of noise leading to misleading interpretations.