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Total Deep Variation for Linear Inverse Problems
TLDR
This paper proposes a novel learnable general-purpose regularizer exploiting recent architectural design patterns from deep learning and casts the learning problem as a discrete sampled optimal control problem, for which the adjoint state equations and an optimality condition are derived.
Time Discrete Geodesic Paths in the Space of Images
TLDR
A robust and effective variational time discretization of geodesics paths is proposed to minimize a discrete path energy consisting of a sum of consecutive image matching functionals over a set of image intensity maps and pairwise matching deformations.
Bayesian Uncertainty Estimation of Learned Variational MRI Reconstruction
TLDR
This work solves the linear inverse problem of undersampled MRI reconstruction in a variational setting and can accurately quantify the pixelwise epistemic uncertainty, which can serve radiologists as an additional resource to visualize reconstruction reliability.
Total Deep Variation: A Stable Regularizer for Inverse Problems
TLDR
This work combines the variational formulation of inverse problems with deep learning by introducing the data-driven general-purpose total deep variation regularizer that allows for a rigorous mathematical analysis including an optimal control formulation of the training problem in a mean-field setting and a stability analysis with respect to the initial values and the parameters of the regularizer.
Joint reconstruction and classification of tumor cells and cell interactions in melanoma tissue sections with synthesized training data
TLDR
A machine learning approach using variational networks for joint image denoising and classification of tissue sections for melanoma, which is an established model tumor for immuno-oncology research, with a particular emphasis on tumor immune cell interactions and on the robust cell nuclei classification is developed.
Time Discrete Extrapolation in a Riemannian Space of Images
The Riemannian metamorphosis model introduced and analyzed in [7, 12] is taken into account to develop an image extrapolation tool in the space of images. To this end, the variational time
GEASI: Geodesic‐based earliest activation sites identification in cardiac models
TLDR
GEASI (Geodesic‐based Earliest Activation Sites Identification) is introduced as a novel approach to simultaneously identify all EASs in cardiac electrical activation and demonstrates the clinical applicability of GEASI for potential future personalized models and clinical intervention.
Variational Networks: An Optimal Control Approach to Early Stopping Variational Methods for Image Restoration
TLDR
A nonlinear spectral analysis of the gradient of the learned regularizer gives enlightening insights into the different regularization properties, and the development of first- and second-order conditions to verify optimal stopping time is developed.
Image Morphing in Deep Feature Spaces: Theory and Applications
TLDR
Numerical experiments indicate that the incorporation of semantic deep features in the metamorphosis model is superior to intensity-based approaches.
Bézier Curves in the Space of Images
TLDR
This paper generalizes the notion of Bezier curves to the infinite-dimensional space of images, equipped with a Riemannian metric which measures the cost of image transport and intensity variation in the sense of the metamorphosis model.
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