Measures of goodness of fit to convolution model for analysis of fMRI data

On an fMRI data analysis, it is common to assume that we know when stimuli were presented or when subjects performed a task. However, for mental tasks such as memory retrieval, we cannot obtain an exact time of the task execution. When we use complex stimuli or natural stimuli such as a movie in experiments, then sometimes we cannot define the presentation time of stimuli straightforwardly. For these cases, we propose measures of a neural activity that we can obtain without a time series of stimuli presentations or task executions. We apply a blind deconvolution algorithm to an fMRI data set and separate it into a Hemodynamic Response Function (HRF) and a series of presentation times of stimuli. We propose to use values of the cost function for this separation algorithm as measures of a neural activity. The cost function is consisted of two terms. One is an error term representing discrepancy from a conventional convolution model of fMRI. The other term represents statistical characteristics of the estimated stimuli presentation time series.