相关论文: Total Variation Denoising on Hexagonal Grids

Although transformer-based models have been dominating the field of deep learning, various studies of their embedding space have shown that they suffer from "representation degeneration problem": embeddings tend to be distributed in a…

We review the theory of, and develop algorithms for transforming a finite point set in ${\bf R}^d$ into a set in \emph{radial isotropic position} by a nonsingular linear transformation followed by rescaling each image point to the unit…

Omnidirectional cameras are widely used in such areas as robotics and virtual reality as they provide a wide field of view. Their images are often processed with classical methods, which might unfortunately lead to non-optimal solutions as…

Total variation (TV) regularization is a classical tool for image denoising, but its convex $\ell_1$ formulation often leads to staircase artifacts and loss of contrast. To address these issues, we introduce the Transformed $\ell_1$ (TL1)…

Purpose: To develop a synergistic image reconstruction framework that exploits multicontrast (MC), multicoil, and compressed sensing (CS) redundancies in magnetic resonance imaging (MRI). Approach: CS, MC acquisition, and parallel imaging…

Vertical decomposition is a widely used general technique for decomposing the cells of arrangements of semi-algebraic sets in ${{\mathbb R}}^d$ into constant-complexity subcells. In this paper, we settle in the affirmative a few…

Optimization techniques have been widely used in deformable registration, allowing for the incorporation of similarity metrics with regularization mechanisms. These regularization mechanisms are designed to mitigate the effects of trivial…

Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural…

A new decomposition optimization algorithm, called \textit{path-following gradient-based decomposition}, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this…

In this paper, we propose a novel symmetric alternating minimization algorithm to solve a broad class of total variation (TV) regularization problems. Unlike the usual $z^k\to x^k$ Gauss-Seidel cycle, the proposed algorithm performs the…

We derive a new lower bound for the bandwidth of a graph that is based on a new lower bound for the minimum cut problem. Our new semidefinite programming relaxation of the minimum cut problem is obtained by strengthening the known…

The 'exact subgraph' approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…

Lifting methods allow to transform hard variational problems such as segmentation and optical flow estimation into convex problems in a suitable higher-dimensional space. The lifted models can then be efficiently solved to a global optimum,…

The advancement of imaging devices and countless image data generated everyday impose an increasingly high demand on efficient and effective image denoising. In this paper, we present a computationally simple denoising algorithm, termed…

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…

Many material response functions depend strongly on microstructure, such as inhomogeneities in phase or orientation. Homogenization presents the task of predicting the mean response of a sample of the microstructure to external loading for…

We consider the very challenging task of restoring images (i) which have a large number of missing pixels, (ii) whose existing pixels are corrupted by noise and (iii) the ideal image to be restored contains both cartoon and texture…

In this paper, we propose a new graph-based transform and illustrate its potential application to signal compression. Our approach relies on the careful design of a graph that optimizes the overall rate-distortion performance through an…

As shown in [15], under some structural assumptions, working on congested traffic problems in general and increasingly dense networks leads, at the limit by {\Gamma}-convergence, to continuous minimization problems posed on measures on…

We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…