Related papers: Coupling local and nonlocal total variation flow f…
Defocus blur is a physical consequence of the optical sensors used in most cameras. Although it can be used as a photographic style, it is commonly viewed as an image degradation modeled as the convolution of a sharp image with a…
Image retouching, aiming to regenerate the visually pleasing renditions of given images, is a subjective task where the users are with different aesthetic sensations. Most existing methods deploy a deterministic model to learn the…
Nonlocal image representation has been successfully used in many image-related inverse problems including denoising, deblurring and deblocking. However, a majority of reconstruction methods only exploit the nonlocal self-similarity (NSS)…
The non-local block is a popular module for strengthening the context modeling ability of a regular convolutional neural network. This paper first studies the non-local block in depth, where we find that its attention computation can be…
Filtering images of more than one channel is challenging in terms of both efficiency and effectiveness. By grouping similar patches to utilize the self-similarity and sparse linear approximation of natural images, recent nonlocal and…
Our work deals with the systematic study of the coupling between the nonlocal Stokes system and the Vlasov equation. The coupling is due to a drag force generated by the fluid-particles interaction. We establish the existence of global weak…
The aim of this paper is to establish a nonlinear variational approach to the reconstruction of moving density images from indirect dynamic measurements. Our approach is to model the dynamics as a hyperelastic deformation of an initial…
Image denoising is a fundamental task in computer vision. While prevailing deep learning-based supervised and self-supervised methods have excelled in eliminating in-distribution noise, their susceptibility to out-of-distribution (OOD)…
Dense visual prediction tasks have been constrained by their reliance on predefined categories, limiting their applicability in real-world scenarios where visual concepts are unbounded. While Vision-Language Models (VLMs) like CLIP have…
We study a natural alternating method of Schwarz type (domain decomposition) for certain class of couplings between local and nonlocal operators. We show that our method fits into Lion's framework and prove, as a consequence, convergence in…
This paper demonstrates a practical method that can correct spatial varying blur from a set of images of the same object. The algorithm jointly estimates the object and local point spread functions~(PSF). The method prioritizes sections…
We develop a microscopic theory of optical absorption and structured-light dichroism in a nonlocal minimal-coupling framework. Starting from the minimal-coupling Hamiltonian, we express absorption as a bilinear functional of the…
Area openings and closings are morphological filters which efficiently suppress impulse noise from an image, by removing small connected components of level sets. The problem of an objective choice of threshold for the area remains open.…
Image deblurring, removing blurring artifacts from images, is a fundamental task in computational photography and low-level computer vision. Existing approaches focus on specialized solutions tailored to particular blur types, thus, these…
In a recent study [DutykhDias2007] we presented a novel visco-potential free surface flows formulation. The governing equations contain local and nonlocal dissipative terms. From physical point of view, local dissipation terms come from…
We study the asymptotic behavior for nonlocal diffusion equations $\partial_tu=\mathcal{J}u-\chi_0u$ in $\mathbb{R}^n\times(0,\infty)$ and obtain a sufficient condition so that solutions of the Cauchy problem decay in time at the rate of a…
Many classic methods have shown non-local self-similarity in natural images to be an effective prior for image restoration. However, it remains unclear and challenging to make use of this intrinsic property via deep networks. In this paper,…
Hyperspectral analysis has gained popularity over recent years as a way to infer what materials are displayed on a picture whose pixels consist of a mixture of spectral signatures. Computing both signatures and mixture coefficients is known…
Denoising is of utmost importance for the visualization and processing of images featuring low signal-to-noise ratio. Total variation methods are among the most popular techniques to perform this task improving the signal-to-noise ratio…
We revisit total variation denoising and study an augmented model where we assume that an estimate of the image gradient is available. We show that this increases the image reconstruction quality and derive that the resulting model…