Related papers: Higher-order Spatial Accuracy in Diffeomorphic Ima…
In this article, we improve the convergence order of some finite volume solutions approximating some second order elliptic problems. We prove that finite volume approximations of order $O(h^{k+1})$, with $k$ integer, can be obtained after…
This paper introduces the use of unbalanced optimal transport methods as a similarity measure for diffeomorphic matching of imaging data. The similarity measure is a key object in diffeomorphic registration methods that, together with the…
The focus of this work is on rigorous mathematical analysis of the topological derivative based detection algorithms for the localization of an elastic inclusion of vanishing characteristic size. A filtered quadratic misfit is considered…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
Numerical analysis for the stochastic Stokes equations is still challenging even though it has been well done for the corresponding deterministic equations. In particular, the pre-existing error estimates of finite element methods for the…
We consider the harmonic map heat flow problem for a corotational case. For discretization of this problem we apply a $H^1$-conforming finite element method in space combined with a semi-implicit Euler time stepping. The semi-implicit Euler…
We study the use of the hybridizable discontinuous Galerkin (HDG) method for numerically solving fractional diffusion equations of order $-\alpha$ with $-1<\alpha<0$. For exact time-marching, we derive optimal algebraic error estimates…
In this paper, we present a new adaptive rank approximation technique for computing solutions to the high-dimensional linear kinetic transport equation. The approach we propose is based on a macro-micro decomposition of the kinetic model in…
We study the hybridizable discontinuous Galerkin (HDG) method for the spatial discretization of time fractional diffusion models with Caputo derivative of order $0<\alpha<1$. For each time $t \in [0,T]$, the HDG approximations are taken to…
We present a registration method for model reduction of parametric partial differential equations with dominating advection effects and moving features. Registration refers to the use of a parameter-dependent mapping to make the set of…
We consider the problem of discretizing one-dimensional, real-valued functions as graphs. The goal is to find a small set of points, from which we can approximate the remaining function values. The method for approximating the unknown…
We introduce a weighted particle representation for the solution of the filtering problem based on a suitably chosen variation of the classical de Finetti theorem. This representation has important theoretical and numerical applications. In…
When applying the finite-differences method to numerically solve the one-dimensional diffusion equation, one must choose discretization steps $\Delta x$, $\Delta t$ in space and time, respectively. By applying large-deviation theory on the…
In this paper, we introduce, in a Hilbert space setting, a second order dynamical system with asymptotically vanishing damping and vanishing Tikhonov regularization that approaches a multiobjective optimization problem with convex and…
In this article, we design and analyze a Hybrid High-Order (HHO) finite element approximation for a class of strongly nonlinear boundary value problems. We consider an HHO discretization for a suitable linearized problem and show its…
Medical image registration is a fundamental and vital task which will affect the efficacy of many downstream clinical tasks. Deep learning (DL)-based deformable image registration (DIR) methods have been investigated, showing…
In this paper, we develop a functional differentiability approach for solving statistical optimal allocation problems. We derive Hadamard differentiability of the value functions through analyzing the properties of the sorting operator…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…
This article is concerned with the numerical solution of subspace optimization problems, consisting of minimizing a smooth functional over the set of orthogonal projectors of fixed rank. Such problems are encountered in particular in…
This work deals with a regularization method enforcing solution sparsity of linear ill-posed problems by appropriate discretization in the image space. Namely, we formulate the so called least error method in an $\ell^1$ setting and perform…