A Mathematical Model for Understanding the STatistical effects of k-space (AMMUST-k) preprocessing on observed voxel measurements in fcMRI and fMRI

Image processing is common in functional magnetic resonance imaging (fMRI) and functional connectivity magnetic resonance imaging (fcMRI). Such processing may have deleterious effects on statistical maps computed from the processed images. In this manuscript, we describe a mathematical framework to evaluate the effects of image processing on observed voxel means, covariances and correlations resulting from linear processes on k-space and image-space data. We develop linear operators for common image processing operations, including: zero-filling, apodization, smoothing and partial Fourier reconstruction; and unmodeled physical processes, including: Fourier encoding anomalies caused by eddy currents, intra-acquisition decay and magnetic field inhomogeneities. With such operators, we theoretically compute the exact image-space means, covariances and correlations which result from their common implementation and verify their behavior in experimental phantom data. Thus, a very powerful framework is described to consider the effects of image processing on observed voxel means, covariances and correlations. With this framework, researchers can theoretically consider observed voxel correlations while understanding the extent of artifactual correlations resulting from image processing. Furthermore, this framework may be utilized in the future to theoretically optimize image acquisition parameters, and examine the order of image processing steps.