相关论文: Total Variation and Euler's Elastica for Supervise…

Deep Learning based methods have emerged as the indisputable leaders for virtually all image restoration tasks. Especially in the domain of microscopy images, various content-aware image restoration (CARE) approaches are now used to improve…

Total Generalized Variation (TGV) regularization in image reconstruction relies on an infimal convolution type combination of generalized first- and second-order derivatives. This helps to avoid the staircasing effect of Total Variation…

This letter addresses the problem of estimating block sparse signal with unknown group partitions in a multiple measurement vector (MMV) setup. We propose a Bayesian framework by applying an adaptive total variation (TV) penalty on the…

This article is the second work in our series of papers dedicated to image processing models based on the fractional order total variation $TV^r$. In our first work of this series, we studied key analytic properties of these semi-norms.…

We propose a neural network-based algorithm for solving forward and inverse problems for partial differential equations in unsupervised fashion. The solution is approximated by a deep neural network which is the minimizer of a cost…

Autoencoder-based learning has emerged as a staple for disciplining representations in unsupervised and semi-supervised settings. This paper analyzes a framework for improving generalization in a purely supervised setting, where the target…

Recent deep learning approaches focus on improving quantitative scores of dedicated benchmarks, and therefore only reduce the observation-related (aleatoric) uncertainty. However, the model-immanent (epistemic) uncertainty is less…

This study presents the development of a spatially adaptive weighting strategy for Total Variation regularization, aimed at addressing under-determined linear inverse problems. The method leverages the rapid computation of an accurate…

In this paper we consider denoising and inpainting problems for higher dimensional combined cyclic and linear space valued data. These kind of data appear when dealing with nonlinear color spaces such as HSV, and they can be obtained by…

We introduce a new class of numerical methods for solving McKean-Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the…

Time series constitute a challenging data type for machine learning algorithms, due to their highly variable lengths and sparse labeling in practice. In this paper, we tackle this challenge by proposing an unsupervised method to learn…

In this work we show that Evolution Strategies (ES) are a viable method for learning non-differentiable parameters of large supervised models. ES are black-box optimization algorithms that estimate distributions of model parameters; however…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

Euler's elastica model has been extensively studied and applied to image processing tasks. However, due to the high nonlinearity and nonconvexity of the involved curvature term, conventional algorithms suffer from slow convergence and high…

We address the Unsupervised Domain Adaptation (UDA) problem in image classification from a new perspective. In contrast to most existing works which either align the data distributions or learn domain-invariant features, we directly learn a…

We consider an image decomposition model involving a variational (minimization) problem and an evolutionary partial differential equation (PDE). We utilize a linear inhomogenuous diffusion constrained and weighted total variation (TV)…

We introduce variational spectral learning (VSL), a machine learning framework for solving partial differential equations (PDEs) that operates directly in the coefficient space of spectral expansions. VSL offers a principled bridge between…

We consider a patch-based learning approach defined in terms of neural networks to estimate spatially adaptive regularisation parameter maps for image denoising with weighted Total Variation (TV) and test it to situations when the noise…

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…

The elastic-net is among the most widely used types of regularization algorithms, commonly associated with the problem of supervised generalized linear model estimation via penalized maximum likelihood. Its nice properties originate from a…