Spatial smoothing in fMRI using prolate spheroidal wave functions

摘要

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. Hum Brain Mapp 2008. © 2007 Wiley‐Liss, Inc.