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Over the past decades, many individual nonconvex methods have been proposed to achieve better sparse recovery performance in various scenarios. However, how to construct a valid nonconvex regularization function remains open in practice. In…

Machine Learning · Statistics 2022-02-16 Zhiyong Zhou

In this paper the problem of recovering a regularized solution of the Fredholm integral equations of the first kind with Hermitian and square-integrable kernels, and with data corrupted by additive noise, is considered. Instead of using a…

Classical Analysis and ODEs · Mathematics 2007-05-23 Enrico De Micheli , Nicodemo Magnoli , Giovanni Alberto Viano

This article addresses the challenge of learning effective regularizers for linear inverse problems. We analyze and compare several types of learned variational regularization against the theoretical benchmark of the optimal affine…

Numerical Analysis · Mathematics 2025-10-15 Sebastian Banert , Christoph Brauer , Dirk Lorenz , Lionel Tondji

In this report, a novel efficient algorithm for recovery of jointly sparse signals (sparse matrix) from multiple incomplete measurements has been presented, in particular, the NESTA-based MMV optimization method. In a nutshell, the jointly…

Information Theory · Computer Science 2009-05-21 Lianlin Li , Fang Li

Ensemble Kalman inversion is a parallelizable methodology for solving inverse or parameter estimation problems. Although it is based on ideas from Kalman filtering, it may be viewed as a derivative-free optimization method. In its most…

Numerical Analysis · Mathematics 2024-12-20 Neil K. Chada , Andrew M. Stuart , Xin T. Tong

Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…

Machine Learning · Statistics 2015-06-05 Yiyuan She , Huanghuang Li , Jiangping Wang , Dapeng Wu

In this work we present a novel optimization strategy for image reconstruction tasks under analysis-based image regularization, which promotes sparse and/or low-rank solutions in some learned transform domain. We parameterize such…

Computer Vision and Pattern Recognition · Computer Science 2023-08-11 Iaroslav Koshelev , Stamatios Lefkimmiatis

In this paper, we investigate regularization of linear inverse problems with irregular noise. In particular, we consider the case that the noise can be preprocessed by certain adjoint embedding operators. By introducing the consequent…

Numerical Analysis · Mathematics 2024-01-30 Xinyan Li , Simon Hubmer , Shuai Lu , Ronny Ramlau

We consider linear sparse recovery problems where additional structure regarding the support of the solution is known. The form of the structure considered is non-overlapping sets of indices that each contain part of the support. An…

Numerical Analysis · Mathematics 2021-10-05 Joseph S. Donato , Howard W. Levinson

Diffusion MRI is a well established imaging modality providing a powerful way to probe the structure of the white matter non-invasively. Despite its potential, the intrinsic long scan times of these sequences have hampered their use in…

Quantitative Methods · Quantitative Biology 2013-12-31 Alessandro Daducci , Dimitri Van De Ville , Jean-Philippe Thiran , Yves Wiaux

The study of solving the inverse eigenvalue problem for nonnegative matrices has been around for decades. It is clear that an inverse eigenvalue problem is trivial if the desirable matrix is not restricted to a certain structure. Provided…

Numerical Analysis · Mathematics 2014-08-13 Matthew M. Lin

In hyperspectral sparse unmixing, a successful approach employs spectral bundles to address the variability of the endmembers in the spatial domain. However, the regularization penalties usually employed aggregate substantial computational…

Computer Vision and Pattern Recognition · Computer Science 2024-01-25 Luciano Carvalho Ayres , Ricardo Augusto Borsoi , José Carlos Moreira Bermudez , Sérgio José Melo de Almeida

While iterative matrix inversion methods excel in computational efficiency, memory optimization, and support for parallel and distributed computing when managing large matrices, their limitations are also evident in multiple-input…

Information Theory · Computer Science 2025-10-17 Jinfei Wang , Yi Ma , Rahim Tafazolli

In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…

Numerical Analysis · Computer Science 2013-01-15 Anastasios Kyrillidis , Volkan Cevher

Random sinusoidal features are a popular approach for speeding up kernel-based inference in large datasets. Prior to the inference stage, the approach suggests performing dimensionality reduction by first multiplying each data vector by a…

Machine Learning · Statistics 2017-07-12 Mohammadreza Soltani , Chinmay Hegde

In this paper, we consider a regularization strategy for the factorization method when there is noise added to the data operator. The factorization method is a qualitative method used in shape reconstruction problems. These methods are…

Analysis of PDEs · Mathematics 2023-04-05 Isaac Harris

This paper introduces a new strategy for setting the regularization parameter when solving large-scale discrete ill-posed linear problems by means of the Arnoldi-Tikhonov method. This new rule is essentially based on the discrepancy…

Numerical Analysis · Mathematics 2013-07-02 Silvia Gazzola , Paolo Novati , Maria Rosaria Russo

Over the past few years, trace regression models have received considerable attention in the context of matrix completion, quantum state tomography, and compressed sensing. Estimation of the underlying matrix from regularization-based…

Machine Learning · Statistics 2015-04-24 Martin Slawski , Ping Li , Matthias Hein

Traditional numerical methods for calculating matrix eigenvalues are prohibitively expensive for high-dimensional problems. Iterative random sparsification methods allow for the estimation of a single dominant eigenvalue at reduced cost by…

Numerical Analysis · Mathematics 2023-10-03 Samuel M. Greene , Robert J. Webber , Timothy C. Berkelbach , Jonathan Weare

We study iterative regularization for linear models, when the bias is convex but not necessarily strongly convex. We characterize the stability properties of a primal-dual gradient based approach, analyzing its convergence in the presence…

Machine Learning · Statistics 2020-10-30 Cesare Molinari , Mathurin Massias , Lorenzo Rosasco , Silvia Villa