Robust estimation of HDR in fMRI using H^∞ 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.