Computational and Mathematical Methods in Medicine
Volume 2013 (2013), Article ID 643129, 11 pages
Research Article

A Mixed L2 Norm Regularized HRF Estimation Method for Rapid Event-Related fMRI Experiments

China National Digital Switching System Engineering and Technological Research Center, Zhengzhou 450002, China

Received 4 January 2013; Revised 26 March 2013; Accepted 8 April 2013

Academic Editor: Lei Ding

Copyright © 2013 Yu Lei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Brain state decoding or “mind reading” via multivoxel pattern analysis (MVPA) has become a popular focus of functional magnetic resonance imaging (fMRI) studies. In brain decoding, stimulus presentation rate is increased as fast as possible to collect many training samples and obtain an effective and reliable classifier or computational model. However, for extremely rapid event-related experiments, the blood-oxygen-level-dependent (BOLD) signals evoked by adjacent trials are heavily overlapped in the time domain. Thus, identifying trial-specific BOLD responses is difficult. In addition, voxel-specific hemodynamic response function (HRF), which is useful in MVPA, should be used in estimation to decrease the loss of weak information across voxels and obtain fine-grained spatial information. Regularization methods have been widely used to increase the efficiency of HRF estimates. In this study, we propose a regularization framework called mixed L2 norm regularization. This framework involves Tikhonov regularization and an additional L2 norm regularization term to calculate reliable HRF estimates. This technique improves the accuracy of HRF estimates and significantly increases the classification accuracy of the brain decoding task when applied to a rapid event-related four-category object classification experiment. At last, some essential issues such as the impact of low-frequency fluctuation (LFF) and the influence of smoothing are discussed for rapid event-related experiments.