Hemodynamic transfer function estimation with Laguerre polynomials and confidence intervals construction, from functional magnetic resonance imaging (fMRI) data

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 offer two contributions here. Firstly 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. Additionally we develop a procedure for providing confidence intervals for the whole HR function. This feature is completely lacking in all previous work.