Related papers: Finite element-based space-time total variation-ty…
The T-wave of an electrocardiogram (ECG) represents the ventricular repolarization that is critical in restoration of the heart muscle to a pre-contractile state prior to the next beat. Alterations in the T-wave reflect various cardiac…
We propose a new joint image reconstruction method by recovering edge directly from observed data. More specifically, we reformulate joint image reconstruction with vectorial total-variation regularization as an $l_1$ minimization problem…
A wide array of image recovery problems can be abstracted into the problem of minimizing a sum of composite convex functions in a Hilbert space. To solve such problems, primal-dual proximal approaches have been developed which provide…
With the regular decomposition technique, we decompose the space $\mathbf{H}_0^s(\mathbf{curl}; \Omega)$ into the sum of a vector potential space and the gradient of a scalar space, both possessing higher regularity. Based on this new high…
In parallel magnetic resonance imaging (pMRI), to find a joint solution for the image and coil sensitivity functions is a nonlinear and nonconvex problem. A class of algorithms reconstruct sensitivity encoded images of the coils first…
This paper presents a finite-volume method, together with fully adaptive multi-resolution scheme to obtain spatial adaptation, and a Runge-Kutta-Fehlberg scheme with a local time-varying step to obtain temporal adaptation, to solve…
We propose a model for restoration of spatio-temporal TIRF images based on infimal decomposition regularization model named STAIC proposed earlier. We propose to strengthen the STAIC algorithm by enabling it to estimate the relative weights…
In two dimensions, we consider the problem of reconstructing a vector field from partial knowledge of its zeroth and first moment ray transforms. Different from existing works the data is known on a subset of lines, namely the ones…
In inverse problems, prior information and a priori-based regularization techniques play important roles. In this paper, we focus on image restoration problems, especially on restoring images whose texture mainly follow one direction. In…
The tractions that cells exert on a gel substrate from the observed displacements is an increasingly attractive and valuable information in biomedical experiments. The computation of these tractions requires in general the solution of an…
A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In addition to being an integral part of bundle adjustment and…
In electrical impedance tomography, algorithms based on minimizing a linearized residual functional have been widely used due to their flexibility and good performance in practice. However, no rigorous convergence results have been…
In this paper we propose and study a novel optimal transport based regularization of linear dynamic inverse problems. The considered inverse problems aim at recovering a measure valued curve and are dynamic in the sense that (i) the…
Reconstructing an image from its Radon transform is a fundamental computed tomography (CT) task arising in applications such as X-ray scans. In many practical scenarios, a full 180-degree scan is not feasible, or there is a desire to reduce…
In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these…
Hybrid inverse problems are based on the interplay of two types of waves, in order to allow for imaging with both high resolution and high contrast. The inversion procedure often consists of two steps: first, internal measurements involving…
Computer-based simulations of non-invasive cardiac electrical outputs, such as electrocardiograms and body surface potential maps, usually entail severe computational costs due to the need of capturing fine-scale processes and to the…
We study iterative finite element approximations for the numerical approximation of semilinear elliptic boundary value problems with monotone nonlinear reactions of subcritical growth. The focus of our contribution is on an optimal a priori…
We discuss the forward and inverse problems between the potential V(x) measured in a heart chamber and its sources represented by a dipole density d(y) located on the heart wall. We show that the mapping from d(y) to V(x) is a compact…
In this paper we formulate and analyze a space-time finite element method for the numerical simulation of rotating electric machines where the finite element mesh is fixed in space-time domain. Based on the Babu\v{s}ka--Ne\v{c}as theory we…