Separability of spatiotemporal spectra of image sequences

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Abstract
We calculated the spatiotemporal power spectrum of 14 image sequences in order to determine the degree to which the spectra are separable in space and time and to assess the validity of the commonly used exponential correlation model found in the literature. We expand the spectrum by a singular value decomposition into a sum of separable terms and define an index of spatiotemporal separability as the fraction of the signal energy that can be represented by the first (largest) separable term. All spectra were found to be highly separable with an index of separability above 0.98. The power spectra of the sequences were well fit by a separable model of the form P(k, f) = ab/(4pi3)/((a/2pi)2 + k2)3/2((b/2pi)2 + f2) where k is radial spatial frequency, f is temporal frequency, and a,b are spatial and temporal model parameters that determine the effective spatiotemporal bandwidth of the signal. This power spectrum model corresponds to a product of exponential autocorrelation functions separable in space and time.

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