Table 1.
Summary of the acquisition parameters for each protocol.
Figure 1.
Averaged values of (a) FA, (b) MD, (c) MK over 2500 trials and their corresponding mean square errors (dāf) for different estimators. The results are shown for the uncorrected noisy signal (red), and for the signal corrected by M1 (green), M2 (blue) and ML (magenta). The black line indicates the reference value.
Figure 2.
Normalized signal attenuation fits before and after noise corrections for the different correction schemes.
The data correspond to a single diffusion direction in WM areas, for two different voxels with apparent SNR values equal to 26.3 (a) and 16.7 (b) respectively.
Table 2.
Kapp and Dapp (10ā3 mm2/s) values for two voxels with different SNR, corresponding to Figure 1, with their standard errors.
Figure 3.
Histograms of diffusion parameters for one slice.
(a) MK map for one single subject (position P1) and one selected slice corrected with method M1. (b) MK, (c) MD and (d) FA histograms of the same slice for uncorrected signal (NC and BM4D+NC) and using various correction schemes (M1, BM4D+M1, M2, BM4D+M2 and ML estimator).
Figure 4.
Map and histograms of MK for high SNR acquisition (P6).
(a) MK map of the selected slice for high SNR acquisition (P6) corrected with M1 and (b) the MK histograms of the same slice for three correction schemes (dashed lines). The corresponding histograms for P1 (low SNR acquisition) are also shown (solid curves). The histograms are practically overlapping after the noise correction (blue and green curves). The non-corrected histograms are shifted with respect to each other. However, the difference between corrected and non-corrected values is smaller for higher SNR.
Figure 5.
SNR and corresponding MK maps for low (P1 to P5) and high (P6) SNR acquisitions.
The first column corresponds to SNR maps calculated as the ratio of the signal in non-DW images and the noise standard deviation. MK maps are shown in the other columns. Each row represents one acquisition with a different SNR profile. Results are shown for non-corrected (BM4D+NC) and corrected (BM4D+M1 and BM4D+M2) data. Results without BM4D filter are similar. The region delineated by a white rectangle is zoomed in Figure 6.
Figure 6.
Zoom of SNR and MK maps for different SNR acquisitions.
This figure corresponds to a zoomed area of Figure 5 for 4 selected positions (P1, P4, P5 and P6) and the same correction schemes (shown in colour for better visualization).
Figure 7.
Averaged MK values for the different correction schemes in two different ROIs.
(a) Right Globus Pallidus and (b) Left Temporal Lobe. Results are shown for the same subject with 6 different levels of SNR corresponding to acquisitions P1 to P6.
Figure 8.
Z-score maps for each correction scheme (rows) and low SNR positions (P1 to P5).
The reference is the average MK map over the 5 positions for each correction schemes. Arrows indicate regions of positive bias of MK due to lower SNR.
Table 3.
Mean MK values and standard deviations for each correction scheme and each ROI. P-values for Pearson correlation with SNR are indicated by: * p<0.05 and ** p<0.01.
Figure 9.
Averaged MK maps over 25 subjects and their standard deviation for one selected slice.
MK maps are shown on first and third rows and the corresponding standard deviation maps on second and fourth rows for (a) NC, (b) M1, (c) M2, (d) BM4D+NC, (e) BM4D+M1, (f) BM4D+M2. (g) Mean SNR maps of the averaged non-DW image.
Figure 10.
Histograms of the MK maps averaged over all subjects.
The averaged histograms are shown for one selected slice (the same as in Figure 9) for the different correction schemes: (a) M1, (b) M2, (c) NC, (d) BM4D+M1, (e) BM4D+M2, (f) BM4D+NC. Black curves represent the whole slice histograms; red and blue curves refer to WM and GM parts, respectively.
Table 4.
Mean MK values and standard deviation over 25 subjects for each correction scheme.
Table 5.
Summary of selected parameters from different published studies used for comparison.