Neural-network theorems state that only when there are infinitely many hidden units is a four-layered feedforward neural network equivalent to a three-layered feedforward neural network. In actual applications, however, the use of infinitely many hidden units is impractical. Therefore, studies should focus on the capabilities of a neural network with a finite number of hidden units, In this paper, a proof is given showing that a three-layered feedforward network with N-1 hidden units can give any N input-target relations exactly. Based on results of the proof, a four-layered network is constructed and is found to give any N input-target relations with a negligibly small error using only (N/2)+3 hidden units. This shows that a four-layered feedforward network is superior to a three-layered feedforward network in terms of the number of parameters needed for the training data.

Purpose:To test whether our proposed denoising approach with deep learning-based reconstruction (dDLR) can effectively denoise brain MR images. Methods:In an initial experimental study, we obtained brain images from five volunteers and added different artificial noise levels. Denoising was applied to the modified images using a denoising convolutional neural network (DnCNN), a shrinkage convolutional neural network (SCNN), and dDLR. Using these brain MR images, we compared the structural similarity (SSIM) index and peak signal-to-noise ratio (PSNR) between the three denoising methods. Two neuroradiologists assessed the image quality of the three types of images. In the clinical study, we evaluated the denoising effect of dDLR in brain images with different levels of actual noise such as thermal noise. Specifically, we obtained 2D-T 2 -weighted image, 2D-fluid-attenuated inversion recovery (FLAIR) and 3D-magnetization-prepared rapid acquisition with gradient echo (MPRAGE) from 15 healthy volunteers at two different settings for the number of image acquisitions (NAQ): NAQ2 and NAQ5. We reconstructed dDLR-processed NAQ2 from NAQ2, then compared with SSIM and PSNR. Two neuroradiologists separately assessed the image quality of NAQ5, NAQ2 and dDLR-NAQ2. Statistical analysis was performed in the experimental and clinical study. In the clinical study, the inter-observer agreement was also assessed. Results:In the experimental study, PSNR and SSIM for dDLR were statistically higher than those of DnCNN and SCNN (P < 0.001). The image quality of dDLR was also superior to DnCNN and SCNN. In the clinical study, dDLR-NAQ2 was significantly better than NAQ2 images for SSIM and PSNR in all three sequences (P < 0.05), except for PSNR in FLAIR. For all qualitative items, dDLR-NAQ2 had equivalent or better image quality than NAQ5, and superior quality to that of NAQ2 (P < 0.05), for all criteria except artifact. The inter-observer agreement ranged from substantial to near perfect.Conclusion: dDLR reduces image noise while preserving image quality on brain MR images.

BACKGROUND AND PURPOSE:Quantitative susceptibility mapping is useful for assessing iron deposition in the substantia nigra of patients with Parkinson disease. We aimed to determine whether quantitative susceptibility mapping is useful for assessing the lateral asymmetry and spatial difference in iron deposits in the substantia nigra of patients with Parkinson disease.

No abstract

No abstract