(1) Psychology Department, Sheffield University, Sheffield, S10 2UR, England.
(2) Wellcome Department of Cognitive Neurology, Queens Square, London, England.
Independent component analysis (ICA)  can be used in two complementary ways to decompose a sequence of images. First, spatial ICA (sICA) finds a set of mutually independent images , whereas temporal ICA (tICA) finds a set of mutually independent time courses. However, it may be physically unrealistic to expect that an image sequence originates from a set of statistically independent images modulated by a dual set of unconstrained time courses, as implied by sICA. Conversely, it may be unrealistic to expect that an image sequence originates from a set of statistically independent time courses modulated by a dual set of unconstrained image basis vectors, as implied by tICA. Neither sICA nor tICA places any constraint on the form of these dual signals, so that the independence of extracted (spatial or temporal) source signals can be achieved at the cost of physically improbable forms for the (temporal or spatial, respectively) dual signals. One way to constrain the solutions found by ICA is to permit a trade-off between the mutual independence of images and the mutual independence of their corresponding time courses. We introduce a method, spatiotemporal ICA (stICA), which simultaneously maximises a measure of independence over time and space. We applied singular value decomposition (SVD), sICA, tICA and stICA to a sequence of 360 fMRI images. Only sICA and stICA isolated the time course associated with the experimental protocol, as well as the corresponding anatomical site of activity.
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