Improving the functional connectivity magnetic resonance imaging (fcMRI) blood oxygenation level dependent (BOLD) signal through the characterization of processing e!ects

The functional connectivity blood oxygenation dependent signal in magnetic resonance imaging is measured by calculating the correlation of voxel time series. As this signal is small, non-negligible processing steps are applied to the acquired data. Some previous studies have developed empirical measures of the effects of such processing steps. In this work, we examine the effects of the processing steps through an exact, analytical framework. We parameterize the process of reconstruction as a linear process on a real-valued isomorphism of the acquired complex valued data. We then develop linear operators to perform standard image processing steps, including: echo planar data censoring, echo planar data reordering, Nyquist ghost elimination, partial Fourier reconstruction, intra-acquisition decay and decay correction, magnetic field inhomogeneity effects and magnetic field inhomogeneity correction, frequencyspace apodization, and image-space smoothing. We further expand the linear framework to include processes which are applied to the acquired time series, including: the extension of image processing operations to temporal image processing operations, dynamic magnetic field correction, dynamic intra-acquisition decay correction, slice timing correction, motion correction, and temporal filtering. In each case of spatial and temporal processing, we analytically demonstrate the effects caused by applying the operators both individually and in groups and illustrate the results in acquired phantom data. The results of the analytical framework correspond well to the empirical results described by others. Finally, we motivate the implementation of the developed operators in experimental functional magnetic resonance imaging and functional connectivity magnetic resonance imaging data.