相关论文: TRIPs-Py: Techniques for Regularization of Inverse…

Optimal transport (OT) is a widely used tool in machine learning, but computing high-accuracy solutions for large instances remains costly. Entropic regularization and the Sinkhorn algorithm improve scalability; however, when the…

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…

The numerical solution of linear discrete ill-posed problems typically requires regularization, i.e., replacement of the available ill-conditioned problem by a nearby better conditioned one. The most popular regularization methods for…

Tikhonov regularization is a widely used technique in solving inverse problems that can enforce prior properties on the desired solution. In this paper, we propose a Krylov subspace based iterative method for solving linear inverse problems…

Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…

Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meaningful solution is to introduce a regularizer. While for most…

Iterative solvers for large-scale linear systems such as Krylov subspace methods can diverge when the linear system is ill-conditioned, thus significantly reducing the applicability of these iterative methods in practice for…

We propose a new exact approach for solving integer linear programming (ILP) problems which we will call projective splitting algorithms (PSAs). Unlike classical methods for solving ILP problems, PSAs conduct the search for the optimal…

The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…

The direpack package aims to establish a set of modern statistical dimension reduction techniques into the Python universe as a single, consistent package. The dimension reduction methods included resort into three categories: projection…

Many physical and engineering systems require solving direct problems to predict behavior and inverse problems to determine unknown parameters from measurement. In this work, we study both aspects for systems governed by differential…

Linear operators and optimisation are at the core of many algorithms used in signal and image processing, remote sensing, and inverse problems. For small to medium-scale problems, existing software packages (e.g., MATLAB, Python numpy and…

Many evolutionary and constructive heuristic approaches have been introduced in order to solve the Traveling Thief Problem (TTP). However, the accuracy of such approaches is unknown due to their inability to find global optima. In this…

Real-world problems are very difficult to optimize. However, many researchers have been solving benchmark problems that have been extensively investigated for the last decades even if they have very few direct applications. The Traveling…

Operator-splitting methods are widespread in the numerical solution of differential equations, especially the initial-value problems in ordinary differential equations that arise from a method-of-lines discretization of partial differential…

Inverse problems are concerned with the reconstruction of unknown physical quantities using indirect measurements and are fundamental across diverse fields such as medical imaging, remote sensing, and material sciences. These problems serve…

Robust estimation provides essential tools for analyzing data that contain outliers, ensuring that statistical models remain reliable even in the presence of some anomalous data. While robust methods have long been available in R, users of…

In this work, we consider ill-posed inverse problems in which the forward operator is continuous and weakly closed, and the sought solution belongs to a weakly closed constraint set. We propose a regularization method based on minimizing…

A recently introduced text classifier, called SS3, has obtained state-of-the-art performance on the CLEF's eRisk tasks. SS3 was created to deal with risk detection over text streams and, therefore, not only supports incremental training and…

Flexible Krylov methods are a common standpoint for inverse problems. In particular, they are used to address the challenges associated with explicit variational regularization when it goes beyond the two-norm, for example involving an…