Fig 1.
The pipeline for constructing DKI phantoms.
Fig 2.
Results of DKI phantom construction.
Top row: original noisy DW images; middle row: DW images of the constructed phantom; bottom row: DW images of the phantom, with synthetic Rician noise (σ = 10). The phantom consists of 151 volumes of DW images, including one baseline and 5 nonzero b-values (b = 500 ~ 2500 s/mm2) for each of 30 different diffusion gradient directions. Parameters of DW images are as follows: (a) b = 1000 s/mm2, at 16th gradient direction, (b) b = 1000 s/mm2 at 1st gradient direction and (c) b = 2000 s/mm2 at 1st gradient direction.
Fig 3.
Quantitative comparison of NLM, VNLM-b and VNLM-d filters using the DKI phantom.
Five levels of Rician noises with standard deviations of 5, 10, 15, 20, and 25 were added to the phantom DW images. The MSE, Bias and Std values of denoised DW images and MK and MD (DKI parameters) maps were calculated and compared. Top row: MSE value, middle row: Bias value, and bottom row: Std value.
Fig 4.
Visual comparison of denoising filters using the DKI phantom.
Top row: DW images of b = 2500 s/mm2; middle row: MK maps; bottom row: MD maps. Images from left to right are ground truth, noisy image (with Rician noise of standard deviation = 10), and results from NLM, VNLM-b and VNLM-d filters.
Fig 5.
Comparison of denoising filters based on DW images (b = 2500 s/mm2) from real DKI dataset.
Dataset of three volunteers are shown from top to bottom. Images from left to right are the original acquired images, and denoised results from NLM, VNLM-b, and VNLM-d filters.
Fig 6.
Comparison of denoising filters based on MK maps.
From visual observation, The MK map from VNLM-d filter is almost free of black holes. The narrow arrows show the regions that more black holes are produced by NLM and VNLM-b filters. The black hole represents incorrectly estimated voxels. The bold arrow shows the more structural details preserved by VNLM-d filter.
Fig 7.
Comparison of denoising filters based on MD maps.
Fig 8.
Comparison of structural similarities between DW images based on DKI phantom.
From left to right, DW images acquired with (a) b = 1000 s/mm2, at 16th gradient direction, (b) b = 1000 s/mm2 at 1st gradient direction and (c) b = 2000 s/mm2 at 1st gradient direction. The top and middle rows show the DW images and their corresponding magnified local regions, respectively; the bottom row shows NLM weight of a center voxel calculated in its surrounding search region. The solid line squares represent neighborhood windows of the center voxel, and the dashed line squares represent respective search regions. (b) and (c) are DW images acquired at the same gradient direction. Although their intensity and contrast is quite different, they have a greater structure similarity. The arrows indicate regions where (b) and (c) show similar structures, but (a) does not.