Statistical Improvement of FMRI by Wavelet Denoising

Introduction: A fast post-processing method for noise reduction particularly
suited for fMRI, termed complex-denoising, is presented. The method is based
on shrinking noisy discrete wavelet transform coeffcients via thresholding.
Unlike previous wavelet application to MR images, the denoising algorithm is
applied, separately, to the two orthogonal sets of the complex MR image. The
norm of the combined data is used to construct the image. With this method,
signal-noise decoupling and Gaussian white noise assumptions used in the
wavelet noise suppression scheme, are better furfilled. Comparison between
complex and traditional wavelet denoising methods shows that the complex-denoising scheme improves the signal-to-noise ratio in low SNR regions. The
method is applied below to fMRI data.
Method: Male Sprague-Da.wley rats were anesthetized with urethane i.p. and
put in a BrukerBiospec 4.7T. A pair of small needle-electrodes were used for
stimulation of the right or the left hindlimb. A 20-mm diameter surface coil was
used using the gradient echo (GE) sequence (TE = 40 ms, TR = 80 ms) with
field of view of 2.56 cm, 1 mm slice thickness and resolution of 64 • 64. The flip
angle was 35 ~ in the cortex and lower in deeper structures.
Data analysis: Two different statistical approaches were used. (1) Cross correlation analysis: each pixel in the data-sets was cross correlated with the stimulus
time course function and a correlation map was performed. A threshold of
C = 0.4, corresponding to P < 0.0001, was used in these maps. The number of
pixels above the threshold was calculated and compared. (2) Principal component analysis (PCA): PCA was performed on the data-sets and the variance of the top three components were compared.
Results: In Fig. I we show an example of the difference in the principal
components and cross-correlation maps obtained with undenoised (original),
complex-denoised and absolute denoised data-sets. The variance of the first
principal component (PC) in the complex-denoised set is about twice the
variance of the corresponding PC in the original set (11.3% vs. 6.5%) while is
little better than the variance of the corresponding PC in the absolute denoising
set (10.6%). The other PCs exhibit a similar relation. Using cross-correlation analysis we obtain similar pattern: The activation areas (correlation above 0.4)
is larger in the complex-denoising set (398 pixels), while their size is reduced in
the absolute denoising set (350 pixels) and become much smaller in the original
set (190 pixels). This is a direct consequence of the SNR improvement in the
denoised data-sets. The variance in the PCs and the number of pixels above
threshold in the cross-correlation maps, in the original and the complex
denoised sets were calculated in seven different fMRI data-sets. On average, we
obtain an increase of 150% (!) in the activation area in the cross-correlation
test, and an average increase of 70% in the variance of the first two PCs and an
increase of 53% in the third PC, in the PCA test.