Statistics and Its Interface

Volume 3 (2010)

Number 1

Adaptive spatial smoothing of fMRI images

Pages: 3 – 13



Martin A. Lindquist (Department of Statistics, Columbia University, New York, NY, U.S.A.)

Ji Meng Loh (Department of Statistics, Columbia University, New York, NY, U.S.A.)

Yu (Ryan) Yue (Department of Statistics and CIS, Baruch College, New York, NY, U.S.A.)


It is common practice to spatially smooth fMRI data prior to statistical analysis and a number of different smoothing techniques have been proposed (e.g., Gaussian kernel filters, wavelets, and prolate spheroidal wave functions). A common theme in all these methods is that the extent of smoothing is chosen independently of the data, and is assumed to be equal across the image. This can lead to problems, as the size and shape of activated regions may vary across the brain, leading to situations where certain regions are under-smoothed, while others are over-smoothed. This paper introduces a novel approach towards spatially smoothing fMRI data based on the use of nonstationary spatial Gaussian Markov random fields (Yue and Speckman, 2009). Our method not only allows the amount of smoothing to vary across the brain depending on the spatial extent of activation, but also enables researchers to study how the extent of activation changes over time. The benefit of the suggested approach is demonstrated by a series of simulation studies and through an application to experimental data.


spatially adaptive smoothing, temporally adaptive smoothing, fMRI, brain imaging, smoothing

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