Table 1.
Recent networks used for MR image denoising and MRA data.
As displayed, all listed works use either conventional loss-functions such as L1 and/or SSIM loss or a 2D version of the Perceptual Loss.
Fig 1.
Example 3D MR images of plant roots and brain vessels.
First column: Plant scanned in the MR system, second column: maximum intensity projections (MIP) of MR root image (top: axial plane, mid.: sagittal plane) and a single slice of the 3D image marked yellow in the sagittal plane (bot.). Next columns, top to bot.: Axial, coronal, and sagittal MIP of an MRA image.
Fig 2.
Maximum Intensity Projections of original and noisy images.
From left to right: Original image, cropped part of original image, cropped part of image with 1%, 5%, 10%, and 20% added noise.
Table 2.
Mean and standard deviation values for the five random seeds used for network training for MRA images and MR root images for the loss functions included in this study.
Best results are underlined. Mean and standard deviation values for the evaluation metrics calculated exclusively on the center image parts as well as std values across test sets are given in the Supporting information S2 and S3 Tables.
Fig 3.
MIP of example 3D MR images of plant roots and brain vessels: Ground truth image and image parts after denoising the image that was disturbed with 10% noise.
Upper row: MIP of whole image. In the second and third row, the marked region is zoomed in. Zoomed part reconstructed with different loss functions. Differences are clearly visible and remarkable differences are marked with an arrow.
Table 3.
Mean and std evaluation metrics for MRA and MR root images for different initializations of the untrained loss network.
As shown, different initializations have a minor impact on the results.
Table 4.
Mean and std SSIM values for different kernel sizes and network depth for MRA (above) and for the MR root dataset (below).
All other evaluation metrics can be found in the Supporting information S4 and S5 Tables. As displayed, differences across network sizes and kernel sizes are small.
Fig 4.
Impact of pooling operations in the uPL on the results (Left: MIP of an example MRA image; and right: MR Root image. The marked region is the region which is displayed in large on the right.)
First row: GT image and zoomed part of GT image. Second row: Reconstructed image of image disturbed with 10% noise with different number of pooling operations in the uPL network. Third row: Difference image between GT and reconstructed image.
Fig 5.
MIP of original image (First row) and denoising results of image disturbed with 10% noise for different denoising networks and the L1-loss (second row) and our uPL.
Remarkable differences are marked with arrows.
Table 5.
Mean and std SSIM values across different random seeds for both datasets calculated.
Underlined are the values for the best loss function. I.e. if uPL outperformed L1-loss for a network architecture, the uPL values are underlined. All other evaluation metrics, std values across the testsets, and evaluation metrics calculated on image parts only are listed in the Supporting information (S6–S10 Tables).