Related papers: On the Development of a Coupled Non-linear Telegra…

Topologically protected waves in the linearly polarized Maxwell's equations with gyrotropic, magneto-optic media were studied a decade ago both computationally and experimentally. This paper develops a robust tight-binding model for this…

This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…

Ground-based imaging systems struggle to achieve diffraction-limited resolution when atmospheric turbulence and photon scarcity act simultaneously. In this regime, conventional adaptive optics, speckle imaging, and blind deconvolution lack…

Painterly image harmonization aims to insert photographic objects into paintings and obtain artistically coherent composite images. Previous methods for this task mainly rely on inference optimization or generative adversarial network, but…

Diffusion models have demonstrated remarkable generative capabilities in image processing tasks. We propose a Sparse condition Temporal Rewighted Integrated Distribution Estimation guided diffusion model (STRIDE) for sparse-view CT…

Text-to-image diffusion models often exhibit degraded performance when generating images beyond their training resolution. Recent training-free methods can mitigate this limitation, but they often require substantial computation or are…

Image restoration aims to recover high-quality images from degraded observations. When the degradation process is known, the recovery problem can be formulated as an inverse problem, and in a Bayesian context, the goal is to sample a clean…

Denoising diffusion models achieved impressive results on several image generation tasks often outperforming GAN based models. Recently, the generative capabilities of diffusion models have been employed for perceptual image compression,…

In this paper, we study the diffusive limit of the steady state radiative heat transfer system for non-homogeneous Dirichlet boundary conditions in a bounded domain with flat boundaries. A composite approximate solution is constructed using…

In quantum chemistry, one of the most important challenges is the static correlation problem when solving the electronic Schr\"odinger equation for molecules in the Born--Oppenheimer approximation. In this article, we analyze the tailored…

In this paper we demonstrate that the framework of nonlinear spectral decompositions based on total variation (TV) regularization is very well suited for image fusion as well as more general image manipulation tasks. The well-localized and…

Sparse-view Computed Tomography (CT) image reconstruction is a promising approach to reduce radiation exposure, but it inevitably leads to image degradation. Although diffusion model-based approaches are computationally expensive and suffer…

We introduce a Trajectory-Based RBF Collocation (TBRBF) method for solving surface advection-diffusion equations on smooth, compact manifolds. TBRBF decouples advection and diffusion by applying a characteristic treatment with a Kansa-type…

Diffusion model-based image restoration (IR) aims to use diffusion models to recover high-quality (HQ) images from degraded images, achieving promising performance. Due to the inherent property of diffusion models, most existing methods…

Image restoration, which aims to recover high-quality images from their corrupted counterparts, often faces the challenge of being an ill-posed problem that allows multiple solutions for a single input. However, most deep learning based…

This work concerns the exponential stabilization of underactuated linear homogeneous systems of m parabolic partial differential equations (PDEs) in cascade (reaction-diffusion systems), where only the first state is controlled either…

The central limit theorem suggests Gaussian convolution as a generic blur model for images. Since Gaussian convolution is equivalent to homogeneous diffusion filtering, one way to deblur such images is to diffuse them backwards in time.…

We study solution techniques for parabolic equations with fractional diffusion and Caputo fractional time derivative, the latter being discretized and analyzed in a general Hilbert space setting. The spatial fractional diffusion is realized…

Partial differential equation (PDE)-governed inverse problems are fundamental across various scientific and engineering applications; yet they face significant challenges due to nonlinearity, ill-posedness, and sensitivity to noise. Here,…

In this work, we present a novel methodology for texture image recognition using a partial differential equation modeling. More specifically, we employ the pseudo-parabolic Buckley-Leverett equation to provide a dynamics to the digital…