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We study variational regularisation methods for inverse problems with imperfect forward operators whose errors can be modelled by order intervals in a partial order of a Banach lattice. We carry out analysis with respect to existence and…

Numerical Analysis · Mathematics 2020-12-25 Leon Bungert , Martin Burger , Yury Korolev , Carola-Bibiane Schoenlieb

There is growing body of learning problems for which it is natural to organize the parameters into matrix, so as to appropriately regularize the parameters under some matrix norm (in order to impose some more sophisticated prior knowledge).…

Machine Learning · Computer Science 2010-10-19 Sham M. Kakade , Shai Shalev-Shwartz , Ambuj Tewari

We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…

Optimization and Control · Mathematics 2022-09-28 Kristian Bredies , Marcello Carioni , Martin Holler

A basis expansion with regularization methods is much appealing to the flexible or robust nonlinear regression models for data with complex structures. When the underlying function has inhomogeneous smoothness, it is well known that…

Methodology · Statistics 2021-02-02 Daeju Kim , Shuichi Kawano , Yoshiyuki Ninomiya

We propose a regularization method to solve a nonlinear ill-posed problem connected to inversion of data gathered by a ground conductivity meter.

Numerical Analysis · Mathematics 2021-09-21 Gian Piero Deidda , Caterina Fenu , Giuseppe Rodriguez

A general method for solving nonlinear ill-posed problems is developed. The method consists of solving a Cauchy problem with a regularized operator and proving that the solution of this problem tends, as time grows, to a solution of the…

Mathematical Physics · Physics 2007-05-23 R. Airapetyan , A. G. Ramm , A. Smirnova

Piecewise constant curvature is a popular kinematics framework for continuum robots. Computing the model parameters from the desired end pose, known as the inverse kinematics problem, is fundamental in manipulation, tracking and planning…

Robotics · Computer Science 2023-05-03 Ke Qiu , Jingyu Zhang , Danying Sun , Rong Xiong , Haojian Lu , Yue Wang

We consider a class of inexact Newton regularization methods for solving nonlinear inverse problems in Hilbert scales. Under certain conditions we obtain the order optimal convergence rate result.

Numerical Analysis · Mathematics 2010-09-21 Qinian Jin , Ulrich Tautenhahn

In this work, an accurate regularization technique based on the Meyer wavelet method is developed to solve the ill-posed backward heat conduction problem with time-dependent thermal diffusivity factor in an infinite "strip". In principle,…

Functional Analysis · Mathematics 2018-04-18 Milad Karimi , Fridoun Moradlou , Mojtaba Hajipour

We consider an optimization problem with strongly convex objective and linear inequalities constraints. To be able to deal with a large number of constraints we provide a penalty reformulation of the problem. As penalty functions we use a…

Optimization and Control · Mathematics 2020-04-29 Angelia Nedich , Tatiana Tatarenko

We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…

Numerical Analysis · Mathematics 2016-08-12 Sergey Voronin , Dylan Mikesell , Guust Nolet

The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…

Numerical Analysis · Mathematics 2020-02-11 Toby Sanders , Rodrigo B. Platte , Robert D. Skeel

Regularization-based approaches for injecting constraints in Machine Learning (ML) were introduced to improve a predictive model via expert knowledge. We tackle the issue of finding the right balance between the loss (the accuracy of the…

Machine Learning · Computer Science 2020-05-22 Michele Lombardi , Federico Baldo , Andrea Borghesi , Michela Milano

Inverse design of morphing slender structures with programmable curvature has significant applications in various engineering fields. Most existing studies formulate it as an optimization problem, which requires repeatedly solving the…

Soft Condensed Matter · Physics 2025-08-28 JiaHao Li , Weicheng Huang , YinBo Zhu , Luxia Yu , Xiaohao Sun , Mingchao Liu , HengAn Wu

The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…

Optimization and Control · Mathematics 2019-11-07 Utkan Candogan , Yong Sheng Soh , Venkat Chandrasekaran

The graph matching problem is a significant special case of the Quadratic Assignment Problem, with extensive applications in pattern recognition, computer vision, protein alignments and related fields. As the problem is NP-hard, relaxation…

Optimization and Control · Mathematics 2025-04-01 Rongxuan Li

Inexact Newton regularization methods have been proposed by Hanke and Rieder for solving nonlinear ill-posed inverse problems. Every such a method consists of two components: an outer Newton iteration and an inner scheme providing…

Numerical Analysis · Mathematics 2011-11-09 Qinian Jin

Unsupervised deep learning approaches have recently become one of the crucial research areas in imaging owing to their ability to learn expressive and powerful reconstruction operators even when paired high-quality training data is scarcely…

Computer Vision and Pattern Recognition · Computer Science 2023-11-30 Marcello Carioni , Subhadip Mukherjee , Hong Ye Tan , Junqi Tang

Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an…

Numerical Analysis · Mathematics 2013-01-01 I. Daubechies , M. Fornasier , I. Loris

In this paper a robust second-order method is developed for the solution of strongly convex l1-regularized problems. The main aim is to make the proposed method as inexpensive as possible, while even difficult problems can be efficiently…

Optimization and Control · Mathematics 2015-01-13 Kimon Fountoulakis , Jacek Gondzio