Related papers: Discrete Total Variation with Finite Elements and …
This paper is devoted to developing and applications of a generalized differential theory of variational analysis that allows us to work in incomplete normed spaces, without employing conventional variational techniques based on…
A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic…
This paper proposes a first-order total variation diminishing (TVD) treatment for coarsening and refining of local timestep size in response to dynamic local variations in wave speeds for nonlinear conservation laws. The algorithm is…
Experimentally acquired microscopy images are unavoidably affected by the presence of noise and other unwanted signals, which degrade their quality and might hide relevant features. With the recent increase in image acquisition rate, modern…
We study time-varying semidefinite programs (TV-SDPs), which are semidefinite programs whose data (and solutions) are functions of time. Our focus is on the setting where the data varies polynomially with time. We show that under a strict…
The systems with small binding energies and widely distributed in space bound-state wave functions are considered. Because the interaction potential is weak and rather localized compared to the characteristic sizes of wave functions of…
Total variation(TV) regularization is applied to X-Ray computed tomography(CT) in an effort to reduce metal artifacts. Tikhonov regularization with $L^2$ data fidelity term and total variation regularization is augmented in this novel model…
Traditional image segmentation methods, such as variational models based on partial differential equations (PDEs), offer strong mathematical interpretability and precise boundary modeling, but often suffer from sensitivity to parameter…
Non-linear spectral decompositions of images based on one-homogeneous functionals such as total variation have gained considerable attention in the last few years. Due to their ability to extract spectral components corresponding to objects…
Total variation (TV) regularization is a popular reconstruction method for ill-posed imaging problems, and particularly useful for applications with piecewise constant targets. However, using TV for medical cone-beam computed X-ray…
For image denoising problems, the structure tensor total variation (STV)-based models show good performances when compared with other competing regularization approaches. However, the STV regularizer does not couple the local information of…
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.…
The total generalized variation (TGV) is a popular regularizer in inverse problems and imaging combining discontinuous solutions and higher order smoothing. In particular, empirical observations suggest that its order two version strongly…
Recently, non-convex regularisation models have been introduced in order to provide a better prior for gradient distributions in real images. They are based on using concave energies $\phi$ in the total variation type functional…
High radiation dose in CT scans increases a lifetime risk of cancer and has become a major clinical concern. Recently, iterative reconstruction algorithms with Total Variation (TV) regularization have been developed to reconstruct CT images…
We consider the problem of minimizing the continuous valued total variation subject to different unary terms on trees and propose fast direct algorithms based on dynamic programming to solve these problems. We treat both the convex and the…
Recently, there has been a lot of research into tensor singular value decomposition (t-SVD) by using discrete Fourier transform (DFT) matrix. The main aims of this paper are to propose and study tensor singular value decomposition based on…
Inference and learning for probabilistic generative networks is often very challenging and typically prevents scalability to as large networks as used for deep discriminative approaches. To obtain efficiently trainable, large-scale and well…
In this paper, we introduce a class of variational inequalities, where the involved function is the sum of an arbitrary given vector and a homogeneous polynomial defined by a tensor; and we call it the tensor variational inequality (TVI).…
Polytopal methods provide a flexible framework for the numerical approximation of partial differential equations on general meshes. Their convergence analysis raises specific challenges due to their inherently non-conforming nature and, in…