Robust Estimation of HDR in fMRI using $H^\infty$ Filters

Estimation and detection of the hemodynamic response (HDR) are of great importance in functional MRI (fMRI) data analysis. In this paper, we propose the use of three
H

^∞
adaptive filters (
finite memory
,
exponentially weighted,
and
time-varying
) for accurate estimation and detection of the HDR. The
H

^∞
approach is used because it safeguards against the worst case disturbances and makes no assumptions on the (statistical) nature of the signals [B. Hassibi and T. Kailath, in
Proc. ICASSP
, 1995, vol. 2, pp. 949-952; T. Ratnarajah and S. Puthusserypady, in
Proc. 8th IEEE Workshop DSP
, 1998, pp. 1483-1487]. Performances of the proposed techniques are compared to the conventional
t
-test method as well as the well-known LMSs and recursive least squares algorithms. Extensive numerical simulations show that the proposed methods result in better HDR estimations and activation detections.