相关论文: Graph- and finite element-based total variation mo…

The total generalized variation extends the total variation by incorporating higher-order smoothness. Thus, it can also suffer from similar discretization issues related to isotropy. Inspired by the success of novel discretization schemes…

The Bayesian inference is widely used in many scientific and engineering problems, especially in the linear inverse problems in infinite-dimensional setting where the unknowns are functions. In such problems, choosing an appropriate prior…

When using the finite element method (FEM) in inverse problems, its discretization error can produce parameter estimates that are inaccurate and overconfident. The Bayesian finite element method (BFEM) provides a probabilistic model for the…

One of the fundamental assumptions of compressive sensing (CS) is that a signal can be reconstructed from a small number of samples by solving an optimization problem with the appropriate regularization term. Two standard regularization…

Tomographic image reconstruction is relevant for many medical imaging modalities including X-ray, ultrasound (US) computed tomography (CT) and photoacoustics, for which the access to full angular range tomographic projections might be not…

Topological optimization finds a material density distribution minimizing a functional of the solution of a partial differential equation (PDE), subject to a set of constraints (typically, a bound on the volume or mass of the material).…

This paper introduces a novel variational approach for image compression motivated by recent PDE-based approaches combining edge detection and Laplacian inpainting. The essential feature is to encode the image via a sparse vector field,…

Based on a nonsmooth coherence condition, we construct and prove the convergence of a forward-backward splitting method that alternates between steps on a fine and a coarse grid. Our focus is a total variation regularised inverse imaging…

In a class of piecewise-constant image segmentation models, we propose to incorporate a weighted difference of anisotropic and isotropic total variation (AITV) to regularize the partition boundaries in an image. In particular, we replace…

Solving inverse problems is central to a variety of important applications, such as biomedical image reconstruction and non-destructive testing. These problems are characterized by the sensitivity of direct solution methods with respect to…

Recently, a fast alternating minimization algorithm for total variation image deblurring (FTVd) has been presented by Wang, Yang, Yin, and Zhang [{\em SIAM J. Imaging Sci.}, 1 (2008), pp. 248--272]. The method in a nutshell consists of a…

Fluorescence molecular tomography (FMT) is an emerging powerful tool for biomedical research. There are two factors that influence FMT reconstruction most effectively. The first one is the regularization techniques. Traditional methods such…

We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…

Tensor train (TT) representation has achieved tremendous success in visual data completion tasks, especially when it is combined with tensor folding. However, folding an image or video tensor breaks the original data structure, leading to…

This study presents a finite difference method (FDM) to model the electromagnetic field propagation in eccentric coaxial waveguides filled with lossy uniaxially anisotropic media. The formulation utilizes conformal transformation to map the…

In the present work we introduce a novel refinement algorithm for two-dimensional elliptic partial differential equations discretized with Virtual Element Method (VEM). The algorithm improves the numerical solution accuracy and the mesh…

Mathematical methods of image inpainting involve the discretization of given continuous models. We present a method that avoids the standard pointwise discretization by modeling known variational approaches, in particular total variation…

Score-based diffusion models in infinite-dimensional function spaces provide a mathematically principled framework for modelling function-valued data, offering key advantages such as resolution invariance and the ability to handle irregular…

We consider the problem of reconstructing 2D images from randomly under-sampled confocal microscopy samples. The well known and widely celebrated total variation regularization, which is the L1 norm of derivatives, turns out to be…

Recovering corrupted images is one of the most challenging problems in image processing. Among various restoration tasks, blind image deblurring has been extensively studied due to its practical importance and inherent difficulty. In this…