Related papers: Adaptive mesh reconstruction: Total Variation Boun…
Total variation (TV) minimization is one of the most important techniques in modern signal/image processing, and has wide range of applications. While there are numerous recent works on the restoration guarantee of the TV minimization in…
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…
While medical imaging typically provides massive amounts of data, the extraction of relevant information for predictive diagnosis remains a difficult challenge. Functional MRI (fMRI) data, that provide an indirect measure of task-related or…
Sampling high-dimensional images is challenging due to limited availability of sensors; scanning is usually necessary in these cases. To mitigate this challenge, snapshot compressive imaging (SCI) was proposed to capture the…
Enlightened from the inverse consideration of the stable continuous-time dynamics evolution, the Variation Evolving Method (VEM) analogizes the optimal solution to the equilibrium point of an infinite-dimensional dynamic system and solves…
Factorized in the lifting structure, the wavelet transform can easily be extended by arbitrary compensation methods. Thereby, the transform can be adapted to displacements in the signal without losing the ability of perfect reconstruction.…
In recent works several authors have proposed the use of precise boundary conditions (BCs) for blurring models and they proved that the resulting choice (Neumann or reflective, anti-reflective) leads to fast algorithms both for deblurring…
We present a meshfree numerical solver for scalar conservation laws in one space dimension. Points representing the solution are moved according to their characteristic velocities. Particle interaction is resolved by purely local particle…
The total variation method is widely used in image noise suppression. However, this method is easy to cause the loss of image details, and it is also sensitive to parameters such as iteration time. In this work, the total variation method…
A novel approach for selecting appropriate reconstructions is implemented to the hyperbolic conservation laws in the high-order local polynomial-based framework, e.g., the discontinuous Galerkin (DG) and flux reconstruction (FR) schemes.…
We propose joining a flexible mesh design with an integrated residual transcription in order to improve the accuracy of numerical solutions to optimal control problems. This approach is particularly useful when state or input trajectories…
A simple analytical model is developed to analyze and explain the complex dynamics of the multi-peak modulation instability spectrum observed in dispersion oscillating optical fibers [M. Droques et al., 37, 4832-4834 Opt. Lett., (2012)]. We…
We explore the use of the recently proposed "total nuclear variation" (TNV) as a regularizer for reconstructing multi-channel, spectral CT images. This convex penalty is a natural extension of the total variation (TV) to vector-valued…
In this study, we propose a class of total variation diminishing (TVD) schemes for solving pseudo-monotone variational inequality arises in elasto-hydrodynamic lubrication point contact problem. A limiter based stable hybrid line splittings…
1D Total Variation (TV) denoising, considering the data fidelity and the Total Variation (TV) regularization, proposes a good restored signal preserving shape edges. The main issue is how to choose the weight $\lambda$ balancing those two…
Combined-resolution simulations are an effective way to study molecular properties across a range of length- and time-scales. These simulations can benefit from adaptive boundaries that allow the high-resolution region to adapt (change size…
This study presents constructions of the space-time Conservation Element and Solution Element (CESE) methods to accommodate adaptive unstructured quadrilateral meshes. Subsequently, a novel algorithm is devised to effectively manage the…
Slope limiters play an essential role in maintaining the non-oscillatory behavior of high-resolution methods for nonlinear conservation laws. The family of minmod limiters serves as the prototype example. Here, we revisit the question of…
This paper introduces a new numerical scheme for a system that includes evolution equations describing a perfect plasticity model with a time-dependent yield surface. We demonstrate that the solution to the proposed scheme is stable under…
In this paper we address the temporal energy growth associated with numerical approximations of the perfectly matched layer (PML) for Maxwell's equations in first order form. In the literature, several studies have shown that a numerical…