Spatial smoothing in fMRI using prolate spheroidal wave functions

The acquisition of functional magnetic resonance imaging (fMRI) data in a finite subset of k-space produces ring-artifacts and 'side lobes' that distort the image. In this article, we explore the consequences of this problem for functional imaging studies, which can be considerable, and propose a solution. The truncation of k-space is mathematically equivalent to convolving the underlying "true" image with a sinc function whose width is inversely related to the amount of truncation. Spatial smoothing with a large enough kernel can eliminate these artifacts, but at a cost in image resolution. However, too little spatial smoothing leaves the ringing artifacts and side lobes caused by k-space truncation intact, leading to a potential decrease in signal-to-noise ratio and statistical power. Thus, to make use of the high-resolution afforded by MRI without introducing artifacts, new smoothing filters are needed that are optimized to correct k-space truncation-related artifacts. We develop a prolate spheroidal wave function (PSWF) filter designed to eliminate truncation artifacts and compare its performance to the standard Gaussian filter in simulations and analysis of fMRI data on a visual-motor task. The PSWF filter effectively corrected truncation artifacts and resulted in more sensitive detection of visual-motor activity in expected brain regions, demonstrating its efficacy.