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We analyse a new notion of total anisotropic higher-order variation which, differently from the Total Generalized Variation by Bredies et al., quantifies for possibly non-symmetric tensor fields their variations at arbitrary order weighted…

Numerical Analysis · Mathematics 2020-01-09 Simone Parisotto , Simon Masnou , Carola-Bibiane Schönlieb

This paper studies sparse spikes deconvolution over the space of measures. We focus our attention to the recovery properties of the support of the measure, i.e. the location of the Dirac masses. For non-degenerate sums of Diracs, we show…

Optimization and Control · Mathematics 2014-09-16 Vincent Duval , Gabriel Peyré

We present a powerful and easy-to-implement algorithm for solving constrained optimization problems that involve $L_1$/total-variation regularization terms, and both equality and inequality constraints. We discuss the relationship of our…

Optimization and Control · Mathematics 2015-05-22 Musa Maharramov , Stewart A. Levin

Scarcity of hydrocarbon resources and high exploration risks motivate the development of high fidelity algorithms and computationally viable approaches to exploratory geophysics. Whereas early approaches considered least-squares…

Optimization and Control · Mathematics 2015-04-21 Stephen Becker , Lior Horesh , Aleksandr Aravkin , Sergiy Zhuk

Offline reinforcement learning (RL) aims to learn an optimal policy from a static dataset, making it particularly valuable in scenarios where data collection is costly, such as robotics. A major challenge in offline RL is distributional…

Machine Learning · Computer Science 2025-07-16 Motoki Omura , Yusuke Mukuta , Kazuki Ota , Takayuki Osa , Tatsuya Harada

A solution algorithm for a special class of optimal control problems subject to an ordinary differential equation is proposed. The controls possess a continuous-or-off structure and are priced by a convex function. Additionally, a total…

Optimization and Control · Mathematics 2026-05-22 Markus Friedemann , Gerd Wachsmuth

Nonparametric methods are widely applicable to statistical inference problems, since they rely on a few modeling assumptions. In this context, the fresh look advocated here permeates benefits from variable selection and compressive…

Machine Learning · Statistics 2015-03-19 Gonzalo Mateos , Georgios B. Giannakis

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…

Numerical Analysis · Mathematics 2020-04-15 Abinash Nayak

Optimal Transport is a useful metric to compare probability distributions and to compute a pairing given a ground cost. Its entropic regularization variant (eOT) is crucial to have fast algorithms and reflect fuzzy/noisy matchings. This…

Statistics Theory · Mathematics 2024-03-12 Francisco Andrade , Gabriel Peyre , Clarice Poon

Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…

Numerical Analysis · Mathematics 2018-01-31 Martin Benning , Martin Burger

For an ill-posed inverse problem, particularly with incomplete and limited measurement data, regularization is an essential tool for stabilizing the inverse problem. Among various forms of regularization, the lp penalty term provides a…

Numerical Analysis · Mathematics 2021-12-23 Jihun Han , Yoonsang Lee

We propose an unsupervised approach for learning end-to-end reconstruction operators for ill-posed inverse problems. The proposed method combines the classical variational framework with iterative unrolling, which essentially seeks to…

Computer Vision and Pattern Recognition · Computer Science 2021-06-08 Subhadip Mukherjee , Marcello Carioni , Ozan Öktem , Carola-Bibiane Schönlieb

We consider composite linear inverse problems where the signal to recover is modeled as a sum of two functions. We study a variational framework formulated as an optimization problem over the pairs of components using two regularization…

Optimization and Control · Mathematics 2026-05-25 Adrian Jarret , Julien Fageot

Near-field extremely large multiple input multiple output (XL-MIMO) breaks the assumptions that make classical super-resolution effective: the receiver acquires only a limited set of compressed pilot observations, while each propagation…

Signal Processing · Electrical Eng. & Systems 2026-04-14 Sajad Daei , Gabor Fodor , Mikael Skoglund

Traveltime tomography is a very effective tool to reconstruct acoustic, seismic or electromagnetic wave speed distribution. To infer the velocity image of the medium from the measurements of first arrivals is a typical example of ill-posed…

Geophysics · Physics 2007-05-23 G. Vignoli , L. Zanzi

The solution of inverse problems is crucial in various fields such as medicine, biology, and engineering, where one seeks to find a solution from noisy observations. These problems often exhibit non-uniqueness and ill-posedness, resulting…

Numerical Analysis · Mathematics 2024-10-21 Markus Haltmeier , Richard Kowar , Markus Tiefenthaler

In this paper we investigate an adaptive discretization strategy for ill-posed linear prob- lems combined with a regularization from a class of semiiterative methods. We show that such a discretization approach in combination with a…

Numerical Analysis · Mathematics 2014-07-22 Wolfgang Erb , Evgeniya V. Semenova

We consider the variational discretization of a linear-quadratic optimal control problem with pointwise control and state constraints. In order to allow for a Fr\'echet smooth norm, the problem is reformulated by means of a reflexive…

Optimization and Control · Mathematics 2010-08-24 Morten Vierling

It is well-known that point sources with sufficient mutual distance can be reconstructed exactly from finitely many Fourier measurements by solving a convex optimization problem with Tikhonov-regularization (this property is sometimes…

Optimization and Control · Mathematics 2023-12-13 Martin Holler , Benedikt Wirth

A central question in modern machine learning and imaging sciences is to quantify the number of effective parameters of vastly over-parameterized models. The degrees of freedom is a mathematically convenient way to define this number of…

Machine Learning · Statistics 2019-11-12 Clarice Poon , Gabriel Peyré