English
Related papers

Related papers: Unsupervised parameter selection for denoising wit…

200 papers

Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of…

Methodology · Statistics 2023-05-09 Andrea Arnold

The widely used nuclear norm heuristic for rank minimization problems introduces a regularization parameter which is difficult to tune. We have recently proposed a method to approximate the regularization path, i.e., the optimal solution as…

Systems and Control · Computer Science 2015-04-22 Niclas Blomberg , Cristian R. Rojas , Bo Wahlberg

We exploit the similarities between Tikhonov regularization and Bayesian hierarchical models to propose a regularization scheme that acts like a distributed Tikhonov regularization where the amount of regularization varies from component to…

Numerical Analysis · Mathematics 2024-04-10 Daniela Calvetti , Erkki Somersalo

We present a method for supervised learning of sparsity-promoting regularizers for denoising signals and images. Sparsity-promoting regularization is a key ingredient in solving modern signal reconstruction problems; however, the operators…

Machine Learning · Computer Science 2023-09-07 Avrajit Ghosh , Michael T. McCann , Madeline Mitchell , Saiprasad Ravishankar

In this paper, we consider the nonlinear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered to reconstruct the estimator from the random noisy…

Statistics Theory · Mathematics 2024-04-09 Abhishake Rastogi

We explore anisotropic regularisation methods in the spirit of [Holler & Kunisch, 14]. Based on ground truth data, we propose a bilevel optimisation strategy to compute the optimal regularisation parameters of such a model for the…

Numerical Analysis · Mathematics 2016-02-04 Martin Benning , Carola-Bibiane Schönlieb , Tuomo Valkonen , Verner Vlačić

As machine learning applications grow increasingly ubiquitous and complex, they face an increasing set of requirements beyond accuracy. The prevalent approach to handle this challenge is to aggregate a weighted combination of requirement…

Machine Learning · Computer Science 2026-01-07 Aneesh Barthakur , Luiz F. O. Chamon

This paper is concerned with the solution of large-scale linear discrete ill-posed problems with error-contaminated data. Tikhonov regularization is a popular approach to determine meaningful approximate solutions of such problems. The…

Numerical Analysis · Mathematics 2016-02-11 Guangxin Huang , Silvia Noschese , Lothar Reichel

In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such…

Neural and Evolutionary Computing · Computer Science 2015-08-26 Rossella Cancelliere , Mario Gai , Patrick Gallinari , Luca Rubini

We introduce a method for fast estimation of data-adapted, spatio-temporally dependent regularization parameter-maps for variational image reconstruction, focusing on total variation (TV)-minimization. Our approach is inspired by recent…

When solving rank-deficient or discrete ill-posed problems by regularization methods, the choice of the regularization parameter is crucial. It is also of interest, the regularization norm used in the selection of the solution. In this…

Numerical Analysis · Mathematics 2024-10-30 Ibrahima Dione

The ever-increasing number of parameters in deep neural networks poses challenges for memory-limited applications. Regularize-and-prune methods aim at meeting these challenges by sparsifying the network weights. In this context we quantify…

Machine Learning · Computer Science 2018-10-30 Enzo Tartaglione , Skjalg Lepsøy , Attilio Fiandrotti , Gianluca Francini

This paper presents a predictive model for estimating regularization parameters of diffeomorphic image registration. We introduce a novel framework that automatically determines the parameters controlling the smoothness of diffeomorphic…

Image and Video Processing · Electrical Eng. & Systems 2022-02-08 Jian Wang , Miaomiao Zhang

We investigate a Tikhonov regularization scheme specifically tailored for shallow neural networks within the context of solving a classic inverse problem: approximating an unknown function and its derivatives within a unit cubic domain…

Numerical Analysis · Mathematics 2024-12-17 Yuanyuan Li , Shuai Lu

The identification of states and parameters from noisy measurements of a dynamical system is of great practical significance and has received a lot of attention. Classically, this problem is expressed as optimization over a class of models.…

In this work we approach attractor neural networks from a machine learning perspective: we look for optimal network parameters by applying a gradient descent over a regularized loss function. Within this framework, the optimal…

Machine Learning · Computer Science 2024-02-21 Elena Agliari , Francesco Alemanno , Miriam Aquaro , Alberto Fachechi

Trajectory optimization using a learned model of the environment is one of the core elements of model-based reinforcement learning. This procedure often suffers from exploiting inaccuracies of the learned model. We propose to regularize…

Machine Learning · Computer Science 2019-12-30 Rinu Boney , Norman Di Palo , Mathias Berglund , Alexander Ilin , Juho Kannala , Antti Rasmus , Harri Valpola

Variational regularization is commonly used to solve linear inverse problems, and involves augmenting a data fidelity by a regularizer. The regularizer is used to promote a priori information and is weighted by a regularization parameter.…

Optimization and Control · Mathematics 2024-01-23 Matthias J. Ehrhardt , Silvia Gazzola , Sebastian J. Scott

One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization, i.e. we consider the adaptive learning of the regularization…

Statistics Theory · Mathematics 2021-01-08 Neil K. Chada , Claudia Schillings , Xin T. Tong , Simon Weissmann

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…

Numerical Analysis · Mathematics 2021-12-22 Paolo Massa , Sara Garbarino , Federico Benvenuto