相关论文: Image Restoration Models with Optimal Transport an…

We propose a new constrained optimization approach to hyperspectral (HS) image restoration. Most existing methods restore a desirable HS image by solving some optimization problem, which consists of a regularization term(s) and a…

In this paper we derive a moment relaxation for large-scale nonsmooth optimization problems with graphical structure and spherical constraints. In contrast to classical moment relaxations for global polynomial optimization that suffer from…

Cross-domain alignment between two sets of entities (e.g., objects in an image, words in a sentence) is fundamental to both computer vision and natural language processing. Existing methods mainly focus on designing advanced attention…

The one-dimensional version of the higher order total variation-based model for image restoration proposed by Chan, Marquina, and Mulet in [4] is analyzed. A suitable functional framework in which the minimization problem is well posed is…

In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…

Optimal transport distances (OT) have been widely used in recent work in Machine Learning as ways to compare probability distributions. These are costly to compute when the data lives in high dimension. Recent work by Paty et al., 2019,…

This article devises a new numerical method for first-order transport problems by using the primal-dual weak Galerkin (PD-WG) finite element method recently developed in scientific computing. The PD-WG method is based on a variational…

It has been hypothesized that the most likely atomic rearrangement mechanism during grain boundary (GB) migration is the one that minimizes the lengths of atomic displacements in the dichromatic pattern. In this work, we recast the problem…

The conjugate gradient (CG) method is commonly used for the rapid solution of least squares problems. In image reconstruction, the problem can be ill-posed and also contaminated by noise; due to this, approaches such as regularization…

Reduced order models (ROMs) are widely used in scientific computing to tackle high-dimensional systems. However, traditional ROM methods may only partially capture the intrinsic geometric characteristics of the data. These characteristics…

Optimal transport (OT) theory focuses, among all maps $T:\mathbb{R}^d\rightarrow \mathbb{R}^d$ that can morph a probability measure onto another, on those that are the ``thriftiest'', i.e. such that the averaged cost $c(x, T(x))$ between…

The L1-norm of the gradient-magnitude images (GMI), which is the well-known total variation (TV) model, is widely used as regularization in the few views CT reconstruction. As the L1-norm TV regularization is tending to uniformly penalize…

In this work, a new constrained hybrid variational deblurring model is developed by combining the non-convex first- and second-order total variation regularizers. Moreover, a box constraint is imposed on the proposed model to guarantee high…

In this paper, we introduce a variant of optimal transport adapted to the causal structure given by an underlying directed graph $G$. Different graph structures lead to different specifications of the optimal transport problem. For…

The main goal of this paper is to propose a new quaternion total variation regularization model for solving linear ill-posed quaternion inverse problems, which arise from three-dimensional signal filtering or color image processing. The…

Matching a source to a target probability measure is often solved by instantiating a linear optimal transport (OT) problem, parameterized by a ground cost function that quantifies discrepancy between points. When these measures live in the…

Although deep neural networks are well-known for their outstanding performance in tackling complex tasks, their hunger for computational resources remains a significant hurdle, posing energy-consumption issues and restricting their…

In the realm of computer vision and graphics, accurately establishing correspondences between geometric 3D shapes is pivotal for applications like object tracking, registration, texture transfer, and statistical shape analysis. Moving…

Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To…

Optimal Transport (OT) has recently emerged as a powerful framework for learning minimal-displacement maps between distributions. The predominant approach involves a neural parametrization of the Monge formulation of OT, typically assuming…