Related papers: An extended Krylov subspace method for decoding ed…
Inpainting-based image compression is a promising alternative to classical transform-based lossy codecs. Typically it stores a carefully selected subset of all pixel locations and their colour values. In the decoding phase the missing…
Krylov subspace, which is generated by multiplying a given vector by the matrix of a linear transformation and its successive powers, has been extensively studied in classical optimization literature to design algorithms that converge…
In spite of the fact that efficient compression methods for dense two-dimensional flow fields would be very useful for modern video codecs, hardly any research has been performed in this area so far. Our paper addresses this problem by…
We consider in this contribution a simplified idealized one-dimensional model in a nuclear core reactor coupling the diffusion equation on the neutron flux withthe enthalpy equation for the water which collects the heat produced by this…
We compare two approaches to compute a portion of the spectrum of dense symmetric definite generalized eigenproblems: one is based on the reduction to tridiagonal form, and the other on the Krylov-subspace iteration. Two large-scale…
Diffusion-based inpainting can reconstruct missing image areas with high quality from sparse data, provided that their location and their values are well optimised. This is particularly useful for applications such as image compression,…
Light incident on a layer of scattering material such as a piece of sugar or white paper forms a characteristic speckle pattern in transmission and reflection. The information hidden in the correlations of the speckle pattern with varying…
Graph coloring is a problem with varied applications in industry and science such as scheduling, resource allocation, and circuit design. The purpose of this paper is to establish if a new gradient based iterative solver framework known as…
The images produced by diffusion models can attain excellent perceptual quality. However, it is challenging for diffusion models to guarantee distortion, hence the integration of diffusion models and image compression models still needs…
Compression methods based on inpainting are an evolving alternative to classical transform-based codecs for still images. Attempts to apply these ideas to video compression are rare, since reaching real-time performance is very challenging.…
This paper presents a hybrid numerical method for linear collisional kinetic equations with diffusive scaling. The aim of the method is to reduce the computational cost of kinetic equations by taking advantage of the lower dimensionality of…
To determine the electron heat flux density on macroscopic scales, the most widely used approach is to solve a diffusion equation through a multi-group technique. This method is however restricted to transport induced by temperature…
We consider the inverse problem of denoising an image where each point (pixel) is an element of a target set, which we refer to as a target-valued image. The target sets considered are either (i) a closed convex set of Euclidean space or…
In recent years, deep learning-based image compression, particularly through generative models, has emerged as a pivotal area of research. Despite significant advancements, challenges such as diminished sharpness and quality in…
The present paper is concerned with developing tensor iterative Krylov subspace methods to solve large multi-linear tensor equations. We use the well-known T-product for two tensors to define tensor global Arnoldi and tensor global…
Integral equation based numerical methods are directly applicable to homogeneous elliptic PDEs, and offer the ability to solve these with high accuracy and speed on complex domains. In this paper, extensions to problems with inhomogeneous…
The discretization of convection-diffusion equations by implicit or semi-implicit methods leads to a sequence of linear systems usually solved by iterative linear solvers such as GMRES. Many techniques bearing the name of \emph{recycling…
In recent years inpainting-based compression methods have been shown to be a viable alternative to classical codecs such as JPEG and JPEG2000. Unlike transform-based codecs, which store coefficients in the transform domain, inpainting-based…
We develop in this note a homogenization method to tackle the problem of a diffusion process through a cracked medium. We show that the cracked surface of the domain induces a source term in the homogenized equation. We assume that the…
A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized finite element method together with a mass lumping technique and an extra…