Related papers: Discrete Total Variation with Finite Elements and …
In this paper, a time-domain discontinuous Galerkin (TDdG) finite element method for the full system of Maxwell's equations in optics and photonics is investigated, including a complete proof of a semi-discrete error estimate. The new…
Numerous total variation (TV) regularizers, engaged in image restoration problem, encode the gradients by means of simple $[-1,1]$ FIR filter. Despite its low computational processing, this filter severely deviates signal's high frequency…
The usage of linear transformations has great relevance for data decorrelation applications, like image and video compression. In that sense, the discrete Tchebichef transform (DTT) possesses useful coding and decorrelation properties. The…
In this work, following the Discrete de Rham (DDR) paradigm, we develop an arbitrary-order discrete divdiv complex on general polyhedral meshes. The construction rests 1) on discrete spaces that are spanned by vectors of polynomials whose…
The paper presents a new method of depth estimation dedicated for free-viewpoint television (FTV). The estimation is performed for segments and thus their size can be used to control a trade-off between the quality of depth maps and the…
In this paper, we introduce the Deep Finite Volume Method (DFVM), an innovative deep learning framework tailored for solving high-order (order \(\geq 2\)) partial differential equations (PDEs). Our approach centers on a novel loss function…
We present a fast algorithm for the total variation regularization of the $3$-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved…
We study \emph{TV regularization}, a widely used technique for eliciting structured sparsity. In particular, we propose efficient algorithms for computing prox-operators for $\ell_p$-norm TV. The most important among these is $\ell_1$-norm…
In this paper we study the structure of solutions of the one dimensional weighted total variation regularisation problem, motivated by its application in signal recovery tasks. We study in depth the relationship between the weight function…
The advantage of using a Discrete Variable Representation (DVR) is that the Hamiltonian of two interacting particles can be constructed in a very simple form. However the DVR Hamiltonian is approximate and, as a consequence, the results…
The TV-Stokes model is a two-step variational method for image denoising that combines the estimation of a divergence-free tangent field with total variation regularization in the first step and then uses that to reconstruct the image 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 the problem of estimating a regression function in the common situation where the number of features is small, where interpretability of the model is a high priority, and where simple linear or additive models fail to provide…
Sparsity exploiting image reconstruction (SER) methods have been extensively used with Total Variation (TV) regularization for tomographic reconstructions. Local TV methods fail to preserve texture details and often create additional…
This paper presents an efficient algorithm to solve total variation (TV) regularizations of images contaminated by a both blur and noise. The unconstrained structure of the problem suggests that one can solve a constrained optimization…
Travel-time tomography forces a trade-off between mesh resolution and stability in which the regularizer choice dominates what can be recovered. We introduce MIMIR, a differentiable framework that represents the 2D velocity field as a…
This paper presents a new and efficient numerical algorithm for the biharmonic equation by using weak Galerkin (WG) finite element methods. The WG finite element scheme is based on a variational form of the biharmonic equation that is…
This letter addresses the problem of estimating block sparse signal with unknown group partitions in a multiple measurement vector (MMV) setup. We propose a Bayesian framework by applying an adaptive total variation (TV) penalty on 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…
The aim of this paper is to compute the explicit solution of the total variation denoising problem corresponding to the characteristic function of a set which is the union of two planar disjoint balls with different radii.