Higher-Order Block Term Decomposition for Spatially Folded fMRI Data

Functional Magnetic Resonance Imaging (fMRI) is a noninvasive technique for studying brain activity, which receives an increasing attention in the last decade or so. During an fMRI experiment, a series of brain images is acquired, while the subject possibly performs a set of tasks responding to external stimuli. Changes in the measured blood-oxygen-level dependent (BOLD) signal are used to examine different types of activation in the brain. There are several objectives in the analysis of fMRI data, the most common of which are the localization of regions of the brain, that are activated by a task, and the determination of the functional brain connectivity [1, 2]. The localization of the activated areas in the human brain is a challenging "cocktail party" problem, where several people are talking (areas activated) simultaneously behind a wall (skull). Our goal is to distinguish those areas (spatial maps) as well as activation patterns (time courses) through some blind source separation (decomposition) method [3, 4]. Each source is the outcome of a combination of a time course with a spatial map. In fMRI studies of the brain function, the structure of the data involves multiple modes, such as trial, task condition, subject, in addition to the intrinsic dimensions of time and space [5].