相关论文: Study on parameter choice methods for the RFMP wit…

We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…

We propose a new method for low-rank approximation of Moore-Penrose pseudoinverses (MPPs) of large-scale matrices using tensor networks. The computed pseudoinverses can be useful for solving or preconditioning of large-scale overdetermined…

Parsimony, including sparsity and low rank, has been shown to successfully model data in numerous machine learning and signal processing tasks. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an…

Many inverse problems include nuisance parameters which, while not of direct interest, are required to recover primary parameters. Structure present in these problems allows efficient optimization strategies - a well known example is…

The simultaneous orthogonal matching pursuit (SOMP) algorithm aims to find the joint support of a set of sparse signals acquired under a multiple measurement vector model. Critically, the analysis of SOMP depends on the maximal inner…

Constrained partially observable Markov decision processes (CPOMDPs) have been used to model various real-world phenomena. However, they are notoriously difficult to solve to optimality, and there exist only a few approximation methods for…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our…

The reduced basis method (RBM) empowers repeated and rapid evaluation of parametrized partial differential equations through an offline-online decomposition, a.k.a. a learning-execution process. A key feature of the method is a greedy…

We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a…

A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the…

There are many uses for linear fitting; the context here is interpolation and denoising of data, as when you have calibration data and you want to fit a smooth, flexible function to those data. Or you want to fit a flexible function to…

Researchers have widely used exploratory factor analysis (EFA) to learn the latent structure underlying multivariate data. Rotation and regularised estimation are two classes of methods in EFA that they often use to find interpretable…

Existing diffusion-based methods for inverse problems sample from the posterior using score functions and accept the generated random samples as solutions. In applications that posterior mean is preferred, we have to generate multiple…

Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…

Two popular examples of first-order optimization methods over linear spaces are coordinate descent and matching pursuit algorithms, with their randomized variants. While the former targets the optimization by moving along coordinates, the…

In this work we deal with parametric inverse problems, which consist in recovering a finite number of parameters describing the structure of an unknown object, from indirect measurements. State-of-the-art methods for approximating a…

This paper introduces new solvers for the computation of low-rank approximate solutions to large-scale linear problems, with a particular focus on the regularization of linear inverse problems. Although Krylov methods incorporating explicit…

Robust low-rank matrix completion (RMC), or robust principal component analysis with partially observed data, has been studied extensively for computer vision, signal processing and machine learning applications. This problem aims to…

We study here sparse recovery problems in the presence of additive noise. We analyze a thresholding version of the CoSaMP algorithm, named Thresholding Greedy Pursuit (TGP). We demonstrate that an appropriate choice of thresholding…