Related papers: An adaptive augmented regularization method and it…
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,…
Recently, the stochastic asymptotical regularization (SAR) has been developed in (\emph{Inverse Problems}, 39: 015007, 2023) for the uncertainty quantification of the stable approximate solution of linear ill-posed inverse problems. In this…
Reliable causal effect estimation from observational data requires adjustment for confounding and sufficient overlap in covariate distributions between treatment groups. However, in high-dimensional settings, lack of overlap often inflates…
Many modern computer vision and machine learning applications rely on solving difficult optimization problems that involve non-differentiable objective functions and constraints. The alternating direction method of multipliers (ADMM) is a…
An overview is given of Bayesian inversion and regularization procedures. In particular, the conceptual basis of the maximum entropy method (MEM) is discussed, and extensions to positive/negative and complex data are highlighted. Other…
This paper introduces a novel variational Bayesian method that integrates Tucker decomposition for efficient high-dimensional inverse problem solving. The method reduces computational complexity by transforming variational inference from a…
In the present work, we present numerical results for an iterative method for solving an optimal control problem with inequality contraints. The method is based on generalized Bregman distances. Under a combination of a source condition and…
The Augmented Lagrangian Method as an approach for regularizing inverse problems received much attention recently, e.g. under the name Bregman iteration in imaging. This work shows convergence (rates) for this method when Morozov's…
Deep unfolding networks have recently emerged as a promising approach for synthetic aperture radar (SAR) imaging. However, baseline unfolding networks, typically derived from iterative reconstruction algorithms such as the alternating…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
Binary observations are often repeated to improve data quality, creating technical replicates. Several scoring methods are commonly used to infer the actual individual state and obtain a probability for each state. The common practice of…
The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or…
We study the Bregman Augmented Lagrangian method (BALM) for solving convex problems with linear constraints. For classical Augmented Lagrangian method, the convergence rate and its relation with the proximal point method is well-understood.…
This paper is devoted to adaptive long autoregressive spectral analysis when (i) very few data are available, (ii) information does exist beforehand concerning the spectral smoothness and time continuity of the analyzed signals. The…
Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown which is augmented by a generalized…
The Alternating Direction Method of Multipliers (ADMM) provides a natural way of solving inverse problems with multiple partial differential equations (PDE) forward models and nonsmooth regularization. ADMM allows splitting these…
In this work, we investigate the use of Besov priors in the context of Bayesian inverse problems. The solution to Bayesian inverse problems is the posterior distribution which naturally enables us to interpret the uncertainties. Besov…
This work presents a Bayesian approach for the estimation of Beta Autoregressive Moving Average ($\beta$ARMA) models. We discuss standard choice for the prior distributions and employ a Hamiltonian Monte Carlo algorithm to sample from the…
Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…
Response-adaptive randomization (RAR) methods can be used to adapt randomization probabilities based on accumulating data, aiming to increase the probability of allocating patients to effective treatments. A popular RAR method is Thompson…