Finite element-based space-time total variation-type regularization of the inverse problem in electrocardiographic imaging

Reconstructing cardiac electrical activity from body surface electric potential measurements results in the severely ill-posed inverse problem in electrocardiography. Many different regularization approaches have been proposed to improve numerical results and provide unique results. This work presents a novel approach for reconstructing the epicardial potential from body surface potential maps based on a space-time total variation-type regularization using finite elements, where a first-order primal-dual algorithm solves the underlying convex optimization problem. In several numerical experiments, the superior performance of this method and the benefit of space-time regularization for the reconstruction of epicardial potential on two-dimensional torso data and a three-dimensional rabbit heart compared to state-of-the-art methods are demonstrated.

Gadolinium dose reduction for brain MRI using conditional deep learning

Recently, deep learning (DL)-based methods have been proposed for the computational reduction of gadolinium-based contrast agents (GBCAs) to mitigate adverse side effects while preserving diagnostic value. Currently, the two main challenges for these approaches are the accurate prediction of contrast enhancement and the synthesis of realistic images. In this work, we address both challenges by utilizing the contrast signal encoded in the subtraction images of pre-contrast and post-contrast image pairs. To avoid the synthesis of any noise or artifacts and solely focus on contrast signal extraction and enhancement from low-dose subtraction images, we train our DL model using noise-free standard-dose subtraction images as targets. As a result, our model predicts the contrast enhancement signal only; thereby enabling synthesization of images beyond the standard dose. Furthermore, we adapt the embedding idea of recent diffusion-based models to condition our model on physical parameters affecting the contrast enhancement behavior. We demonstrate the effectiveness of our approach on synthetic and real datasets using various scanners, field strengths, and contrast agents.

Faithful Synthesis of Low-dose Contrast-enhanced Brain MRI Scans using Noise-preserving Conditional GANs

Today Gadolinium-based contrast agents (GBCA) are indispensable in Magnetic Resonance Imaging (MRI) for diagnosing various diseases. However, GBCAs are expensive and may accumulate in patients with potential side effects, thus dose-reduction is recommended. Still, it is unclear to which extent the GBCA dose can be reduced while preserving the diagnostic value -- especially in pathological regions. To address this issue, we collected brain MRI scans at numerous non-standard GBCA dosages and developed a conditional GAN model for synthesizing corresponding images at fractional dose levels. Along with the adversarial loss, we advocate a novel content loss function based on the Wasserstein distance of locally paired patch statistics for the faithful preservation of noise. Our numerical experiments show that conditional GANs are suitable for generating images at different GBCA dose levels and can be used to augment datasets for virtual contrast models. Moreover, our model can be transferred to openly available datasets such as BraTS, where non-standard GBCA dosage images do not exist.

Shared Prior Learning of Energy-Based Models for Image Reconstruction

We propose a novel learning-based framework for image reconstruction particularly designed for training without ground truth data, which has three major building blocks: energy-based learning, a patch-based Wasserstein loss functional, and shared prior learning. In energy-based learning, the parameters of an energy functional composed of a learned data fidelity term and a data-driven regularizer are computed in a mean-field optimal control problem. In the absence of ground truth data, we change the loss functional to a patch-based Wasserstein functional, in which local statistics of the output images are compared to uncorrupted reference patches. Finally, in shared prior learning, both aforementioned optimal control problems are optimized simultaneously with shared learned parameters of the regularizer to further enhance unsupervised image reconstruction. We derive several time discretization schemes of the gradient flow and verify their consistency in terms of Mosco convergence. In numerous numerical experiments, we demonstrate that the proposed method generates state-of-the-art results for various image reconstruction applications--even if no ground truth images are available for training.

On the estimation of the Wasserstein distance in generative models

Generative Adversarial Networks (GANs) have been used to model the underlying probability distribution of sample based datasets. GANs are notoriuos for training difficulties and their dependence on arbitrary hyperparameters. One recent improvement in GAN literature is to use the Wasserstein distance as loss function leading to Wasserstein Generative Adversarial Networks (WGANs). Using this as a basis, we show various ways in which the Wasserstein distance is estimated for the task of generative modelling. Additionally, the secrets in training such models are shown and summarized at the end of this work. Where applicable, we extend current works to different algorithms, different cost functions, and different regularization schemes to improve generative models.