Related papers: Adaptive mesh reconstruction: Total Variation Boun…
The total variation (TV) flow generates a scale-space representation of an image based on the TV functional. This gradient flow observes desirable features for images, such as sharp edges and enables spectral, scale, and texture analysis.…
Compressed sensing (CS) methods in magnetic resonance imaging (MRI) offer rapid acquisition and improved image quality but require iterative reconstruction schemes with regularization to enforce sparsity. Regardless of the difficulty in…
Recently, total variation (TV) based minimization algorithms have achieved great success in compressive sensing (CS) recovery for natural images due to its virtue of preserving edges. However, the use of TV is not able to recover the fine…
We consider inverse problems with large null spaces, which arise in important applications such as in inverse ECG and EEG procedures. Standard regularization methods typically produce solutions in or near the orthogonal complement of the…
In many inverse problems it is essential to use regularization methods that preserve edges in the reconstructions, and many reconstruction models have been developed for this task, such as the Total Variation (TV) approach. The associated…
A new adaptive weighted essentially non-oscillatory WENO-$\theta$ scheme in the context of finite difference is proposed. Depending on the smoothness of the large stencil used in the reconstruction of the numerical flux, a parameter…
We present compact semi-implicit finite difference schemes on structured grids for numerical solutions of the advection by an external velocity and by a speed in normal direction that are applicable in level set methods. The most involved…
We present in this work a new reconstruction scheme, so-called MUSCL-THINC-BVD scheme, to solve the five-equation model for interfacial two phase flows. This scheme employs the traditional shock capturing MUSCL (Monotone Upstream-centered…
A generalization of implicit conservative numerics to multiple dimensions requires advanced concepts of tensor analysis and differential geometry and hence a more thorough dedication to mathematical fundamentals than maybe expected at first…
The problem of restoration of digital images from their degraded measurements plays a central role in a multitude of practically important applications. A particularly challenging instance of this problem occurs in the case when the…
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups…
An energy-conserving and an energy-and-enstrophy conserving numerical schemes are derived, by approximating the Hamiltonian formulation, based on the Poisson brackets and the vorticity-divergence variables, of the inviscid shallow water…
We present a novel approach to the analysis of a full model of scalar modulation instability (MI) by means of a simple geometrical description in the power vs. frequency plane. This formulation allows to relate the shape of the MI gain to…
Estimating the causal effect of time-varying treatments on survival outcomes is a challenging task in many domains, particularly in medicine where treatment protocols adapt over time. While recent advances in representation learning have…
This paper proposes a computationally efficient algorithm to address the Full-Waveform Inversion (FWI) problem with a Total Variation (TV) constraint, designed to accurately reconstruct subsurface properties from seismic data. FWI, as an…
In this paper we generalize to non-uniform grids of quad-tree type the Compact WENO reconstruction of Levy, Puppo and Russo (SIAM J. Sci. Comput., 2001), thus obtaining a truly two-dimensional non-oscillatory third order reconstruction with…
This work presents a novel interpolation-free mesh adaptation technique for the Euler equations within the arbitrary Lagrangian Eulerian framework. For the spatial discretization, we consider a residual distribution scheme, which provides a…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
We consider the imaging problem of the reconstruction of a three-dimensional object via optical diffraction tomography under the assumptions of the Born approximation. Our focus lies in the situation that a rigid object performs an…
Adaptive techniques are crucial for successful numerical modeling of gravitational waves from astrophysical sources such as coalescing compact binaries, since the radiation typically has wavelengths much larger than the scale of the…