Lowpass temporal filtering in FMRI time series

Neurolmage

11, Number

5, 2000,

Part 2 of 2 Parts 1 D Ebl@

METHODS

- ANALYSIS

Lowpass Temporal Filtering in FMRI Time Series Peter Bannister, David Flitney, Mark Woo&h,

Stephen Smith

FMRIB (Oxford Centre for Functional MRI of the Brain) Lowpass temporal filtering of PMRI dam is a commonly applied preprocessing step. It is applied primarily to reduce noise, and also, in some cases, to precondition the data in order to allow certain assumptions to he made in later statistical analysis. This abstract presents the results of testing some linear and nonlinear filtering methods, with evaluation on real null data with added artificial activation. The results reveal that for PMRI signals with a high level of activation, one of the nonlinear methods provides the most qualitatively accurate signal recovery, (although noise reduction is not really necessary), whilst for lower levels of activation, the matched Gaussian filter (used widely by default) is significantly better than nonlinear filters, and slightly better than no filtering at all. In the light of recent developments in statistical analysis [Woohich et al., KBM2000, submitted], it may therefore not be necessary to carry out lowpass temporal filtering. Filters

Tested:

The following filters were evaluated: 1) No filtering; 2) Butterworth lowpass filter (linear); 3) “HRP-Matched” lowpass filter (Gaussian of HWHM 2.8s) (linear); 4) Wavelet-based (SureShrink [Donoho and Johnstone, Adapting to unknown smoothness via wavelet shrinkage, J. American Statistical Association, 19951, VisuShrink [Donoho and Johnstone, Biometrika, 81:425-455,1994] and Change-point [Ogden and Parzen, Change-point approach to data analytic wavelet thresholding, Statistics and Computing, 19951) (nonlinear); 5) SUSAN noise reduction [Smith and Brady, IJCV, 23(l), 19971 (nonlinear). The wavelet methods work by estimating a point in wavelet-space that separates signal from noise, and using this to attempt to eliminate noise whilst preserving underlying signal. SUSAN noise reduction preserves image/signal structure by only smoothing over neighhours which form part of the same region (i.e., have similar intensity) as the central pixel under consideration. SUSAN has been shown to perform better than many other algorithms, including anisotropic diffusion [Gerig et al., IBEE TMI, 11, 19921, in reducing noise whilst preserving underlying structure. Comparison

Methods:

In order to quantify a filter’s ability to recover activation from a noisy signal, we require some prior knowledge of the nature and location of the activity we are trying to detect. Therefore a synthetic sample dam set was generated by adding artificial activations to a real “null” PMRI data set acquired at 3T with TR=3s. (Because signal is added relative to the noise levels, the results are not dependent on this field strength.) A square wave convolved with a gamma function (in order to mimic a typical BOLD response) was added to a 160-volume resting series at three different activation levels so that the activation constituted 5%, 2% and 1.5% of the signal intensity. (The high-frequency noise level had an approximate standard deviation of 0.5% of the signal level.) Before adding the activation the raw data was motion-corrected using AIR and highpass filtered with a Butterworth filter. The activation was applied into grey matter areas as four 4x4x4 voxel cubes. Spatial filtering was not carried out as it was not the subject of investigation, and is effectively independent of the considerations included here. After each temporal filter had been applied, an unpaired t-test was run on the data to give a z-statistic image. This image was then binary-thresholded at a particular significance level, reflecting the proportion of activation within the original data. Because lowpass filtering violates standard parametric assumptions, the z-statistic is not Gaussian with unit variance. Therefore lowpass filtering was applied to both original and artificially activated data sets, statistical analysis applied to both, and the results from the former used to norm&e the significance levels of the latter. Results

and Conclusions:

Quantitative testing on the 5% and 2% activation data gave close to perfect thresholded images for all filters. Qualitative comparisons revealed that SUSAN exhibited the most appealing signal recovery. At 1.5% activation, when a false positive rate of 10 voxels per volume was selected, the number of false negatives were: unfiltered: 17, matched: 13, Butterworth: 14, SureShrink: 18, Changepoint:21, VisuShrink:26, SUSAN:21. Thus the linear methods are better than no filtering, whilst the nonlinear methods are worse. Thus, whilst SUSAN performs the best at higher levels of activation, at lower levels, all the nonlinear methods tried thus far were not successful. It is interesting, and perhaps surprising, that at high noise levels the non-linear methods were worse than linear ones, i.e. unable to discriminate robustly between “noise” and “signal”. Clearly much work remains to be done, both in testing other filtering methods, and in terms of creating even more realistic data sets for which the optimal analysis output is known. It may be possible to improve the results for the matched filter further by suitably manipulating its parameters. Acknowledgementsz The authors

thank

the UK MRC

and EPSRC

for funding.

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