Related papers: Some remarks on the staircasing phenomenon in tota…
We consider the problem of reconstructing a discrete-time signal (sequence) with continuous-valued components corrupted by a known memoryless channel. When performance is measured using a per-symbol loss function satisfying mild regularity…
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…
The total generalized variation extends the total variation by incorporating higher-order smoothness. Thus, it can also suffer from similar discretization issues related to isotropy. Inspired by the success of novel discretization schemes…
In the pattern matching approach to imaging science, the process of ``metamorphosis'' is template matching with dynamical templates. Here, we recast the metamorphosis equations of into the Euler-Poincare variational framework of and show…
Algorithms for automatically selecting a scalar or locally varying regularization parameter for total variation models with an $L^{\tau}$-data fidelity term, $\tau\in \{1,2\}$, are presented. The automated selection of the regularization…
2D Total Variation Denoising (TVD) is a widely used technique for image denoising. It is also an important nonparametric regression method for estimating functions with heterogenous smoothness. Recent results have shown the TVD estimator to…
We prove mixing on a general class of rank-one transformations containing all known examples of rank-one mixing, including staircase transformations and Ornstein's constructions, and a variety of new constructions.
The recent statistical theory of neural networks focuses on nonparametric denoising problems that treat randomness as additive noise. Variability in image classification datasets does, however, not originate from additive noise but from…
Double diffusive staircases are investigated experimentally in a fluid layer with a stabilizing temperature gradient and a destabilizing gradient of ion concentration. Gradients of temperature and ion concentration are maintained in a…
We present empirical evidence that the range of random time series associated with the tangled nature model of evolution exhibits a devils staircase like behavior characterized by logarithmic trend and the universal multi-affine spectrum of…
We develop a new method for visualizing and refining the invariances of learned representations. Specifically, we test for a general form of invariance, linearization, in which the action of a transformation is confined to a low-dimensional…
Generalization to unseen degradations remains a fundamental challenge for low-level vision models. This paper aims to investigate the underlying mechanism of this failure, using image deraining as a primary case study due to its…
We consider the image denoising problem using total variation (TV) regularization. This problem can be computationally challenging to solve due to the non-differentiability and non-linearity of the regularization term. We propose an…
The problem of restoration of digital images from their degraded measurements plays a central role in a multitude of practically important applications. A particularly challenging instance of this problem occurs in the case when the…
We consider whether minimizers for total variation regularization of linear inverse problems belong to $L^\infty$ even if the measured data does not. We present a simple proof of boundedness of the minimizer for fixed regularization…
We address the problem of optimal scale-dependent parameter learning in total variation image denoising. Such problems are formulated as bilevel optimization instances with total variation denoising problems as lower-level constraints. For…
The success of denoising diffusion models raises important questions regarding their generalisation behaviour, particularly in high-dimensional settings. Notably, it has been shown that when training and sampling are performed perfectly,…
Total variation regularization and total variation flows (TVF) have been widely applied for image enhancement and denoising. To include a generic preservation of crossing curvilinear structures in TVF we lift images to the homogeneous space…
Recently, total variation (TV) based minimization algorithms have achieved great success in compressive sensing (CS) recovery for natural images due to its virtue of preserving edges. However, the use of TV is not able to recover the fine…
We consider total variation minimization for manifold valued data. We propose a cyclic proximal point algorithm and a parallel proximal point algorithm to minimize TV functionals with $\ell^p$-type data terms in the manifold case. These…