相关论文: Non-smooth variational regularization for processi…
Recently, non-convex regularisation models have been introduced in order to provide a better prior for gradient distributions in real images. They are based on using concave energies $\phi$ in the total variation type functional…
Problems in machine learning (ML) can involve noisy input data, and ML classification methods have reached limiting accuracies when based on standard ML data sets consisting of feature vectors and their classes. Greater accuracy will…
Modern signal and image acquisition systems are able to capture data that is no longer real-valued, but may take values on a manifold. However, whenever measurements are taken, no matter whether manifold-valued or not, there occur tiny…
A class of mixed-order \emph{PDE}-constraint regularizer for image processing problem is proposed, generalizing the standard first order total variation $(TV)$. A semi-supervised (bilevel) training scheme, which provides a simultaneous…
Variational methods for revealing visual concepts learned by convolutional neural networks have gained significant attention during the last years. Being based on noisy gradients obtained via back-propagation such methods require the…
We propose two new variational models aimed to outperform the popular total variation (TV) model for image restoration with L$_2$ and L$_1$ fidelity terms. In particular, we introduce a space-variant generalization of the TV regularizer,…
We propose a novel discrete concept for the total generalized variation (TGV), which has originally been derived to reduce the staircasing effect in classical total variation (TV) regularization, in image denoising problems. We describe…
In a number of tomographic applications, data cannot be fully acquired, resulting in a severely underdetermined image reconstruction. In such cases, conventional methods lead to reconstructions with significant artifacts. To overcome these…
We introduce a class of higher-order anisotropic total variation regularisers, which are defined for possibly inhomogeneous, smooth elliptic anisotropies, that extends the Total Generalized Variation (TGV) regulariser and its variants. We…
The total variation (TV) flow generates a scale-space representation of an image based on the TV functional. This gradient flow observes desirable features for images, such as sharp edges and enables spectral, scale, and texture analysis.…
We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and…
In this paper we demonstrate that the framework of nonlinear spectral decompositions based on total variation (TV) regularization is very well suited for image fusion as well as more general image manipulation tasks. The well-localized and…
In electrical impedance tomography, we aim to solve the conductivity within a target body through electrical measurements made on the surface of the target. This inverse conductivity problem is severely ill-posed, especially in real…
During the inversion of discrete linear systems noise in data can be amplified and result in meaningless solutions. To combat this effect, characteristics of solutions that are considered desirable are mathematically implemented during…
This work aims to explore the regularity properties of the smoothed-TV regularization for the functions is of the class H\"older continuous. Over some compact and convex domain $\Omega,$ we study construction of multivariate function…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
Over the last decade or so, reconstruction methods using $\ell_1$ regularization, often categorized as compressed sensing (CS) algorithms, have significantly improved the capabilities of high fidelity imaging in electron tomography. The…
We propose a second-order total generalized variation (TGV) regularization for the reconstruction of the initial condition in variational data assimilation problems. After showing the equivalence between TGV regularization and the Bayesian…
Distributions measured in high energy physics experiments are usually distorted and/or transformed by various detector effects. A regularization method for unfolding these distributions is re-formulated in terms of the Singular Value…
Total Generalized Variation (TGV) has recently been introduced as penalty functional for modelling images with edges as well as smooth variations. It can be interpreted as a "sparse" penalization of optimal balancing from the first up to…