A novel image space formalism of Fourier domain interpolation neural networks for noise propagation analysis

Purpose: To develop an image space formalism of multi-layer convolutional neural networks (CNNs) for Fourier domain interpolation in MRI reconstructions and analytically estimate noise propagation during CNN inference. Theory and Methods: Nonlinear activations in the Fourier domain (also known as k-space) using complex-valued Rectifier Linear Units are expressed as elementwise multiplication with activation masks. This operation is transformed into a convolution in the image space. After network training in k-space, this approach provides an algebraic expression for the derivative of the reconstructed image with respect to the aliased coil images, which serve as the input tensors to the network in the image space. This allows the variance in the network inference to be estimated analytically and to be used to describe noise characteristics. Monte-Carlo simulations and numerical approaches based on auto-differentiation were used for validation. The framework was tested on retrospectively undersampled invivo brain images. Results: Inferences conducted in the image domain are quasi-identical to inferences in the k-space, underlined by corresponding quantitative metrics. Noise variance maps obtained from the analytical expression correspond with those obtained via Monte-Carlo simulations, as well as via an auto-differentiation approach. The noise resilience is well characterized, as in the case of classical Parallel Imaging. Komolgorov-Smirnov tests demonstrate Gaussian distributions of voxel magnitudes in variance maps obtained via Monte-Carlo simulations. Conclusion: The quasi-equivalent image space formalism for neural networks for k-space interpolation enables fast and accurate description of the noise characteristics during CNN inference, analogous to geometry-factor maps in traditional parallel imaging methods.

Joint MR sequence optimization beats pure neural network approaches for spin-echo MRI super-resolution

Current MRI super-resolution (SR) methods only use existing contrasts acquired from typical clinical sequences as input for the neural network (NN). In turbo spin echo sequences (TSE) the sequence parameters can have a strong influence on the actual resolution of the acquired image and have consequently a considera-ble impact on the performance of the NN. We propose a known-operator learning approach to perform an end-to-end optimization of MR sequence and neural net-work parameters for SR-TSE. This MR-physics-informed training procedure jointly optimizes the radiofrequency pulse train of a proton density- (PD-) and T2-weighted TSE and a subsequently applied convolutional neural network to predict the corresponding PDw and T2w super-resolution TSE images. The found radiofrequency pulse train designs generate an optimal signal for the NN to perform the SR task. Our method generalizes from the simulation-based optimi-zation to in vivo measurements and the acquired physics-informed SR images show higher correlation with a time-consuming segmented high-resolution TSE sequence compared to a pure network training approach.

Scale-Equivariant Deep Learning for 3D Data

The ability of convolutional neural networks (CNNs) to recognize objects regardless of their position in the image is due to the translation-equivariance of the convolutional operation. Group-equivariant CNNs transfer this equivariance to other transformations of the input. Dealing appropriately with objects and object parts of different scale is challenging, and scale can vary for multiple reasons such as the underlying object size or the resolution of the imaging modality. In this paper, we propose a scale-equivariant convolutional network layer for three-dimensional data that guarantees scale-equivariance in 3D CNNs. Scale-equivariance lifts the burden of having to learn each possible scale separately, allowing the neural network to focus on higher-level learning goals, which leads to better results and better data-efficiency. We provide an overview of the theoretical foundations and scientific work on scale-equivariant neural networks in the two-dimensional domain. We then transfer the concepts from 2D to the three-dimensional space and create a scale-equivariant convolutional layer for 3D data. Using the proposed scale-equivariant layer, we create a scale-equivariant U-Net for medical image segmentation and compare it with a non-scale-equivariant baseline method. Our experiments demonstrate the effectiveness of the proposed method in achieving scale-equivariance for 3D medical image analysis. We publish our code at https://github.com/wimmerth/scale-equivariant-3d-convnet for further research and application.

Accelerated and Quantitative 3D Semisolid MT/CEST Imaging using a Generative Adversarial Network (GAN-CEST)

Purpose: To substantially shorten the acquisition time required for quantitative 3D chemical exchange saturation transfer (CEST) and semisolid magnetization transfer (MT) imaging and allow for rapid chemical exchange parameter map reconstruction. Methods: Three-dimensional CEST and MT magnetic resonance fingerprinting (MRF) datasets of L-arginine phantoms, whole-brains, and calf muscles from healthy volunteers, cancer patients, and cardiac patients were acquired using 3T clinical scanners at 3 different sites, using 3 different scanner models and coils. A generative adversarial network supervised framework (GAN-CEST) was then designed and trained to learn the mapping from a reduced input data space to the quantitative exchange parameter space, while preserving perceptual and quantitative content. Results: The GAN-CEST 3D acquisition time was 42-52 seconds, 70% shorter than CEST-MRF. The quantitative reconstruction of the entire brain took 0.8 seconds. An excellent agreement was observed between the ground truth and GAN-based L-arginine concentration and pH values (Pearson's r > 0.97, NRMSE < 1.5%). GAN-CEST images from a brain-tumor subject yielded a semi-solid volume fraction and exchange rate NRMSE of 3.8$\pm$1.3% and 4.6$\pm$1.3%, respectively, and SSIM of 96.3$\pm$1.6% and 95.0$\pm$2.4%, respectively. The mapping of the calf-muscle exchange parameters in a cardiac patient, yielded NRMSE < 7% and SSIM > 94% for the semi-solid exchange parameters. In regions with large susceptibility artifacts, GAN-CEST has demonstrated improved performance and reduced noise compared to MRF. Conclusion: GAN-CEST can substantially reduce the acquisition time for quantitative semisolid MT/CEST mapping, while retaining performance even when facing pathologies and scanner models that were not available during training.

snapshot CEST++ : the next snapshot CEST for fast whole-brain APTw imaging at 3T

CEST suffers from two main problems long acquisitin times or restricted coverage as well as incoherent protocol settings. In this paper we give suggestions on how to optimise your protocol settings fro CEST and present one setting for APT CEST. To increase the coverage while keeping the acquisition time constant we suggest using a spatial temporal Compressed Sensing approach. Finally, 1.8mm isotropic whole brain APT CEST maps can be acquired in a little bit less than 2min with a fully integrated online reconstruction. This will pave the way to an even further clinical use of CEST.