相关论文: On the identification of piecewise constant coeffi…

Topological features play an essential role in ensuring geometric plausibility and structural consistency in image analysis tasks such as segmentation and skeletonization. However, integrating topology-preserving learning based on simple…

In this work, an inverse problem on the determination of multiple coefficients arising from the time-domain diffuse optical tomography with fluorescence (DOT-FDOT) is investigated. We simultaneously recover the distribution of background…

The nonlinear convection terms in the governing equations of compressible fluid flows are hyperbolic in nature and are nontrivial for modelling and numerical simulation. Many numerical methods have been developed in the last few decades for…

This paper is devoted to the error analysis of a time-spectral algorithm for fractional diffusion problems of order $\alpha$ ($0 < \alpha < 1$). The solution regularity in the Sobolev space is revisited, and new regularity results in the…

We develop unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \partial_t u-\mathfrak{L}[\varphi(u)]=f(x,t) \qquad\text{in}\qquad \mathbb{R}^N\times(0,T), $$…

In this work we consider the identifiability of two coefficients $a(u)$ and $c(x)$ in a quasilinear elliptic partial differential equation from observation of the Dirichlet-to-Neumann map. We use a linearization procedure due to Isakov [On…

This work is concerned with the recovery of piecewise constant images from noisy linear measurements. We study the noise robustness of a variational reconstruction method, which is based on total (gradient) variation regularization. We show…

We consider the multidimensional space-fractional diffusion equations with spatially varying diffusivity and fractional order. Significant computational challenges are encountered when solving these equations due both to the kernel…

Given $iid$ observations from an unknown absolute continuous distribution defined on some domain $\Omega$, we propose a nonparametric method to learn a piecewise constant function to approximate the underlying probability density function.…

Our aim is to study the backward problem, i.e. recover the initial data from the terminal observation, of the subdiffusion with time dependent coefficients. First of all, by using the smoothing property of solution operators and a…

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…

Accurate detection and segmentation of anatomical structures from ultrasound images are crucial for clinical diagnosis and biometric measurements. Although ultrasound imaging has been widely used with superiorities such as low cost and…

Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. In this work we introduce a new fractional operator…

Diffusion models (DMs) have become the dominant paradigm of generative modeling in a variety of domains by learning stochastic processes from noise to data. Recently, diffusion denoising bridge models (DDBMs), a new formulation of…

This paper is concerned with backward problem for nonlinear space fractional diffusion with additive noise on the right-hand side and the final value. To regularize the instable solution, we develop some new regularized method for solving…

We present multiscale graph-based reduction algorithms for upscaling heterogeneous and anisotropic diffusion problems. The proposed coarsening approaches begin by constructing a partitioning of the computational domain into a set of…

We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…

Convolutional neural networks (CNNs) show outstanding performance in many image processing problems, such as image recognition, object detection and image segmentation. Semantic segmentation is a very challenging task that requires…

We consider numerical methods for linear parabolic equations in one spatial dimension having piecewise constant diffusion coefficients defined by a one parameter family of interface conditions at the discontinuity. We construct immersed…

This paper is concerned with a family of second-order elliptic systems in divergence form with rapidly oscillating periodic coefficients. We initiate the study of homogenization and boundary layers for Neumann problems with first-order…