Figure 6.

Spatial resolution evaluated from the twenty images reconstructed by the five SRR methods on the clinical data set in terms of partial volume effect (PVE). (A) The average PVE achieved by the five methods are, respectively: IAA = 19.40 ± 11.85%, TV = 9.02 ± 7.30%, NLU = 11.35 ± 7.69%, SRCNN =10.88 ± 7.46%, Ours = 7.25 ± 4.37%. Our approach offered a considerably lower percentage of the voxels suffering from PVE in the HR reconstructions than the four baselines, leading to substantially enhanced spatial resolution. Two-sample t-test at the 5% significance level showed that our approach significantly outperformed IAA (p = 1.40e⁻⁶), NLU (p = 2.65e⁻⁴), and SRCNN (p = 5.39e⁻⁴). Wilcoxon signed-rank tests, where the null hypothesis was the difference of two sets of data comes from a distribution with zero median, showed that the population mean rank of our approach significantly differed from the baselines in PVE at the 5% significance level (rejected the null hypothesis with p = 8.86e⁻⁵ for IAA, p = 2.76e⁻² for TV, p = 1.89e⁻⁴ for NLU, and p = 2.93e⁻⁴ for SRCNN). (B) The demonstration of the PVE estimation on a representative image. The curve with a square marker shows the voxel distribution of the image. The dotted lines depict the three Gaussian components in the GMM. The solid line addresses the fitted GMM. The three components from left to right represented the voxels from GM, WM, and CSF, respectively. The difference in the area under the curve between the voxel distribution and the fitted GMM in the range between two successive components corresponded to the estimate of the PVE.