## Abstract

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.

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.

Original language | American English |
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State | Published - 1999 |

Event | ESMRMB'99. 16th Annual meeting of the European Society of Magnetic Resonance in Medicine and Biology - Seville, Spain Duration: 16 Sep 1999 → 19 Sep 1999 |

### Conference

Conference | ESMRMB'99. 16th Annual meeting of the European Society of Magnetic Resonance in Medicine and Biology |
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Country/Territory | Spain |

City | Seville |

Period | 16/09/99 → 19/09/99 |