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.