arXiv:2608.22302v1 Announce Type: new Abstract: The case when a partial differential equation (PDE) can be considered as an Euler-Lagrange (E-L) equation of an energy functional, consisting of a data...
The paper introduces a tensor‑based functional for targeted image enhancement and denoising, incorporating application‑dependent and contextual information through explicit regularization. It establishes existence of a minimizer and discusses tensor symmetry constraints, convexity, and geometric interpretation. The framework demonstrates strong performance in nonlinear scenarios like gamma correction and targeted value‑range filtering, achieving results comparable to state‑of‑the‑art PDE‑based methods.
arXiv:2609.25429v1 Announce Type: new Abstract: In this paper, we introduce the Directional Total Variation-Regularized Implicit Neural Representation (DTV-INR), an advanced variational paradigm that...
arXiv:2608.29227v1 Announce Type: new Abstract: In this work we propose a novel non-linear diffusion filtering approach for images based on their channel representation. To derive the diffusion updat...
arXiv:2605.11585v2 Announce Type: replace Abstract: This paper addresses the problem of image denoising for grayscale images. We propose a probabilistic image generative model that combines a quadtre...
arXiv:2608.22314v1 Announce Type: new Abstract: Many image processing methods such as corner detection, optical flow and iterative enhancement make use of image tensors. Generally, these tensors are...
arXiv:2609.00036v2 Announce Type: replace Abstract: The total scaled-gradient variation (TSGV) regularizer, derived from sparse modeling of piecewise-linear structures, has been shown to preserve edg...
arXiv:2609.00036v1 Announce Type: new Abstract: The total scaled-gradient variation (TSGV) regularizer, derived from sparse modeling of piecewise-linear structures, has been shown to preserve edges a...
arXiv:2509.02109v3 Announce Type: replace-cross Abstract: The Expectation-Maximisation (EM) algorithm is a central tool in statistics and machine learning, widely used for latent-variable models such...
The article reviews how spatially adaptive regularisation weight functions can be incorporated into variational image reconstruction models like Total Variation and Total Generalised Variation. It discusses the regularity properties of these weights—constant, continuous, or piecewise constant—and how they influence edge and detail preservation. The authors highlight recent hybrid methods that learn low‑regularity weights via deep neural networks, demonstrating their effectiveness in image denoising and MRI reconstruction.
arXiv:2602. 02241v2 Announce Type: replace Abstract: Entropic optimal transport (EOT) in continuous spaces with quadratic cost is a classical tool for solving the domain translation problem.
arXiv:2607. 02003v1 Announce Type: cross Abstract: Although neural networks are remarkably effective, their underlying optimization principles remain theoretically elusive, often characterized by non-convex landscapes and stochastic heuristics.