Related papers: On a coupled PDE model for image restoration
In this work, we propose the Haar wavelet method for the coupled degenerate reaction-diffusion PDEs and the ODEs having non-linear a source with Neumann boundary, applicable in various fields of the natural sciences, engineering, and…
This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using Helmholtz decomposition, we reduce the initial-boundary value…
In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…
Edge devices, such as cameras and mobile units, are increasingly capable of performing sophisticated computation in addition to their traditional roles in sensing and communicating signals. The focus of this paper is on collaborative object…
In this paper the use of nonlinear cross-diffu\-sion systems to model image restoration is investigated, theoretically and numerically. In the first case, well-posedness, scale-space properties and long time behaviour are analyzed. From a…
Starting from a variational formulation, we present a model for image segmentation that employs both region statistics and edge information. This combination allows for improved flexibility, making the proposed model suitable to process a…
We consider visual domains in which a class label specifies the content of an image, and class-irrelevant properties that differentiate instances constitute the style. We present a domain-independent method that permits the open-ended…
In this work, we consider an optimal control problem subject to a nonlinear PDE constraint and apply it to the regularized $p$-Laplace equation. To this end, a reduced unconstrained optimization problem in terms of the control variable is…
This paper addresses the problem of correlation estimation in sets of compressed images. We consider a framework where images are represented under the form of linear measurements due to low complexity sensing or security requirements. We…
We propose a new approach for the image super-resolution (SR) task that progressively restores a high-resolution (HR) image from an input low-resolution (LR) image on the basis of a neural ordinary differential equation. In particular, we…
Techniques are developed for decoupling dissipative differential equations. The approach considered is based upon obtaining a sufficient gap in the time dependent linear portion of the equation that corresponds to the linear variational…
Various imaging modalities allow for time-dependent image reconstructions from measurements where its acquisition also has a time-dependent nature. Magnetic particle imaging (MPI) falls into this class of imaging modalities and it thus also…
Image restoration is the task of recovering a clean image from a degraded version. In most cases, the degradation is spatially varying, and it requires the restoration network to both localize and restore the affected regions. In this…
Diffusion models have recently gained traction as a powerful class of deep generative priors, excelling in a wide range of image restoration tasks due to their exceptional ability to model data distributions. To solve image restoration…
Inpainting based image compression approaches, especially linear and non-linear diffusion models, are an active research topic for lossy image compression. The major challenge in these compression models is to find a small set of…
Sampling from Diffusion Models can alternatively be seen as solving differential equations, where there is a challenge in balancing speed and image visual quality. ODE-based samplers offer rapid sampling time but reach a performance limit,…
Ultra-high-definition (UHD) image restoration often faces computational bottlenecks and information loss due to its extremely high resolution. Existing studies based on Variational Autoencoders (VAE) improve efficiency by transferring the…
We construct a local in time, exponentially decaying solution of the one-dimensional variable coefficient Schrodinger equation by solving a nonstandard boundary value problem. A main ingredient in the proof is a new commutator estimate…
We propose a time domain decomposition approach to optimal control of partial differential equations (PDEs) based on semigroup theoretic methods. We formulate the optimality system consisting of two coupled forward-backward PDEs, the state…
In this paper we consider a boundary stabilization problem for the wave equation with interior delay. We prove an exponential stability result under some Lions geometric condition. The proof of the main result is based on an identity with…