Related papers: Numerical Reconstruction of Diffusion and Potentia…
We analyze a reaction coefficient identification problem for the spectral fractional powers of a symmetric, coercive, linear, elliptic, second-order operator in a bounded domain $\Omega$. We realize fractional diffusion as the…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…
This paper addresses the estimation of uncertain distributed diffusion coefficients in elliptic systems based on noisy measurements of the model output. We formulate the parameter identification problem as an infinite dimensional…
The continuum-scale electrokinetic porous-media flow and excess charge redistribution equations are uncoupled using eigenvalue decomposition. The uncoupling results in a pair of independent diffusion equations for "intermediate" potentials…
This paper is dedicated to addressing the simultaneous inversion problem involving the initial value and space-dependent source term in a time-fractional diffusion-wave equation. Firstly, we establish the uniqueness of the inverse problem…
In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…
Image restoration aims to enhance low quality images, producing high quality images that exhibit natural visual characteristics and fine semantic attributes. Recently, the diffusion model has emerged as a powerful technique for image…
We study two numerical approximations of solutions of nonlocal diffusion evolution problems which are inspired in algorithms for computing the bilateral denoising filtering of an image, and which are based on functional rearrangements and…
This article is a review on basic concepts and tools devoted to a posteriori error estimation for problems solved with the Finite Element Method. For the sake of simplicity and clarity, we mostly focus on linear elliptic diffusion problems,…
Rectification and diffusion of non-interacting self-propelled particles is numerically investigated in a two-dimensional corrugated channel. From numerical simulations, we obtain the average velocity and the effective diffusion coefficient.…
We propose a new semiparametric approach for modelling nonlinear univariate diffusions, where the observed process is a nonparametric transformation of an underlying parametric diffusion (UPD). This modelling strategy yields a general class…
We present a systematic study of the reconstruction of a non-negative function via maximum entropy approach utilizing the information contained in a finite number of moments of the function. For testing the efficacy of the approach, we…
A framework for reconstruction of optical diffusion and absorption coefficients in quantitative photoacoustic tomography is presented. This framework is based on a Tikhonov-type functional with a regularization term promoting sparsity of…
Deconvolution of astronomical images is a key aspect of recovering the intrinsic properties of celestial objects, especially when considering ground-based observations. This paper explores the use of diffusion models (DMs) and the Diffusion…
We propose a new fast algorithm for simultaneous recovery of the coil sensitivities and of the magnetization image from incomplete Fourier measurements in parallel MRI. Our approach is based on a parameter model for the coil sensitivities…
As a simplified model for subsurface flows elliptic equations may be utilized. Insufficient measurements or uncertainty in those are commonly modeled by a random coefficient, which then accounts for the uncertain permeability of a given…
This paper presents PolyDiffuse, a novel structured reconstruction algorithm that transforms visual sensor data into polygonal shapes with Diffusion Models (DM), an emerging machinery amid exploding generative AI, while formulating…
Diffusion models have been demonstrated as powerful deep learning tools for image generation in CT reconstruction and restoration. Recently, diffusion posterior sampling, where a score-based diffusion prior is combined with a likelihood…
Previous raw image-based low-light image enhancement methods predominantly relied on feed-forward neural networks to learn deterministic mappings from low-light to normally-exposed images. However, they failed to capture critical…
Diffusion models have marked a significant breakthrough in the synthesis of semantically coherent images. However, their extensive noise estimation networks and the iterative generation process limit their wider application, particularly on…