Untrained perceptual loss for image denoising of line-like structures in MR images

In the acquisition of Magnetic Resonance (MR) images shorter scan times lead to higher image noise. Therefore, automatic image denoising using deep learning methods is of high interest. In this work, we concentrate on image denoising of MR images containing line-like structures such as roots or vessels. In particular, we investigate if the special characteristics of these datasets (connectivity, sparsity) benefit from the use of special loss functions for network training. We hereby translate the Perceptual Loss to 3D data by comparing feature maps of untrained networks in the loss function. We tested the performance of untrained Perceptual Loss (uPL) on 3D image denoising of MR images displaying brain vessels (MR angiograms - MRA) and images of plant roots in soil. In this study, 536 MR images of plant roots in soil and 450 MRA images are included. The plant root dataset is split to 380, 80, and 76 images for training, validation, and testing. The MRA dataset is split to 300, 50, and 100 images for training, validation, and testing. We investigate the impact of various uPL characteristics such as weight initialization, network depth, kernel size, and pooling operations on the results. We tested the performance of the uPL loss on four Rician noise levels (1%, 5%, 10%, and 20%) using evaluation metrics such as the Structural Similarity Index Metric (SSIM). Our results are compared with the frequently used L1 loss for different network architectures. We observe, that our uPL outperforms conventional loss functions such as the L1 loss or a loss based on the Structural Similarity Index Metric (SSIM). For MRA images the uPL leads to SSIM values of 0.93 while L1 and SSIM loss led to SSIM values of 0.81 and 0.88, respectively. The uPL network's initialization is not important (e.g. for MR root images SSIM differences of 0.01 occur across initializations, while network depth and pooling operations impact denoising performance slightly more (SSIM of 0.83 for 5 convolutional layers and kernel size 3 vs. 0.86 for 5 convolutional layers and kernel size 5 for the root dataset). We also find that small uPL networks led to better or comparable results than using large networks such as VGG (e.g. SSIM values of 0.93 and 0.90 for a small and a VGG19 uPL network in the MRA dataset). In summary, we demonstrate superior performance of our loss for both datasets, all noise levels, and three network architectures. In conclusion, for images containing line-like structures, uPL is an alternative to other loss functions for 3D image denoising. We observe that small uPL networks have better or equal performance than very large network architectures while requiring lower computational costs and should therefore be preferred.