Frequently Asked Questions - Smoothing
1. What is smoothing?
2. What's the point of smoothing?
Improving your signal to noise ratio. That's it, in a nutshell. This happens on a couple of levels, both the single-subject and the group.
At the single-subject level: fMRI data has a lot of noise in it, but studies have shown that most of the spatial noise is (mostly) Gaussian - it's essentially random, essentially independent from voxel to voxel, and roughly centered around zero. If that's true, then if we average our intensity across several voxels, our noise will tend to average to zero, whereas our signal (which is some non-zero number) will tend to average to something non-zero, and presto! We've decreased our noise while not decreasing our signal, and our SNR is better. (Desmond & Glover (DesignPapers) demonstrate this effect with real data.)
Matthew Brett has a nice discussion and several illustrations of this on the Cambridge Imagers page: http://www.mrc-cbu.cam.ac.uk/Imaging/smoothing.html
At the group level: Anatomy is highly variable between individuals, and so is exact functional placement within that anatomy. Even with normalized data, there'll be some good chunk of variability between subjects as to where a given functional cluster might be. Smoothing will blur those clusters and thus maximize the overlap between subjects for a given cluster, which increases our odds of detecting that functional cluster at the group level and increasing our sensitivity.
3. When should you smooth? When should you not?
Smoothing is a good idea if:
- You're using SPM, and you want to use p-values corrected with Gaussian field theory (as opposed to FDR).
Smoothing'd not a good idea if:
4. At what point in your analysis stream should you smooth?
The first point at which it's obvious to smooth is as the last spatial preprocessing step for your raw images; smoothing before then will only reduce the accuracy of the earlier preprocessing (normalization, realignment, etc.) - those programs that need smooth images do their own smoothing in memory as part of the calculation, and don't save the smoothed versions. One could also avoid smoothing the raw images entirely and instead smooth the beta and/or contrast images. In terms of efficiency, there's not much difference - smoothing even hundreds of raw images is a very fast process. So the question is one of performance - which is better for your sensitivity?
5. How do you determine the size of your kernel? Based on your resolution? Or structure size?
A little of both, it seems. The matched filter theorem, from the signal processing field, tells us that if we're trying to recover a signal (like an activation) in noisy data (like fMRI), we can best do it by smoothing our data with a kernel that's about the same size as our activation.
Trouble is, though, most of us don't know how big our activations are going to be before we run our experiment. Even if you have a particular structure of interest (say, the hippocampus), you may not get activation over the whole region - only a part.
Given that ambiguity, Skudlarski et. al introduce a method called multifiltering, in which you calculate results once from smoothed images, and then a second set of results from unsmoothed images. Finally, you average together the beta/con images from both sets of results to create a final set of results. The idea is that the smoothed set of results preferentially highlight larger activations, while the unsmoothed set of results preserve small activations, and the final set has some of the advantages of both. Their evaluations showed multifiltering didn't detect larger activations (clusters with radii of 3-4 voxels or greater) as well as purely smoothed results (as you might predict) but that over several cluster sizes, multifiltering outperformed traditional smoothing techniques. Its use in your experiment depends on how important you consider detecting activations of small size (less than 3-voxel radius, or about).
Overall, Skudlarski et. al found that over several cluster sizes, a kernel size of 1-2 voxels (3-6 mm, in their case) was most sensitive in general.
6. Should you use a different kernel for different parts of the brain?
It's an interesting question. Hopfinger et. al find that a 6mm kernel works best for the data they examine in the cortex, but a larger kernel (10mm) works best in subcortical regions. This might be counterintuitive, considering the subcortical structures they examine are small in general than large cortical activations - but they unfortunately don't include information about the size of their activation clusters, so the results are difficult to interpret. You might think a smaller kernel in subcortical regions would be better, due to the smaller size of the structures.
7. What does it actually do to your activation data?
8. What does it do to ROI data?
9. What is Smoove-ing?