With separability assumed, we decompose a three-dimensional point spread function (3D PSF) into two-dimensional (2D) PSFs and further into one-dimensional (ID) PSFs. Based on the observation of the location invariance of a step edge under convolution, we propose a rectification procedure to automatically establish the step-edge function from a blurred edge profile. The ID PSF is modelled as a single-parameter Gaussian function, which is determined by iteratively blurring a step-edge function into a spread edge profile. A plastic solid ball (diameter approximately 6 mm) is used to provide double-edged rectangular functions along scanlines passing through the ball centre, and correspondingly, the reconstructed digital volume provides the blurred rectangular profiles. Experimenting with a cone-beam computed tomography system, we demonstrate the iterative edge-blurring algorithm for PSF measurement. By repositioning the ball phantom in the object support space, we measure the system's spatial variance in terms of full-width-at-half-maximum (FWHM) of the local PSFs. Specifically, we obtained the FWHMs for three specific locations at (0, 0, -40 mm), (0, 0, 0) and (0, 0, 40 mm), which are given by 0.92 +/- 0.10 mm, 0.65 +/- 0.08 mm and 0.93 +/- 0.10 mm, respectively.
Functional magnetic resonance imaging (fMRI) data are acquired as a complex image pair including magnitude and phase information. The vast majority of fMRI experiments do not attempt to take advantage of the time varying phase information. The phase of the MRI signal is related to the local magnetic field changes, suggesting it may contain useful information about the source of hemodynamic activity. Analysis of phase data acquired from different fMRI experiments has shown the presence of activity in response to various stimuli. However, there have been no studies that have examined phase data in a larger group of subjects for multiple types of fMRI tasks nor have studies examined phase changes due to event-related stimuli. In this paper, we evaluate the correspondence between the magnitude and phase changes at a group level in a block-design motor tapping task and in an event-related auditory oddball task. The results for both block-design and event-related tasks indicate the presence of task-related information in the phase data with phase-only and magnitude-only approaches showing signal changes in the expected brain regions. Although there is more overall activity detected with magnitude data, the phase-only analysis also reveals activity in regions expected to be involved in the task, some of which were not significantly activated in the magnitude-only analysis, suggesting that the phase might provide some unique information. In addition, the phase can potentially increase sensitivity within regions also showing magnitude changes. Future work should focus on additional methods for combining the magnitude and phase data.
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