Unfolding is the ensemble of techniques aimed at resolving inverse, ill-posed problems. A pedagogical introduction to the origin and main problems related to unfolding is presented and used as the the stepping stone towards the illustration of some of the most common techniques that are currently used in particle physics experiments.

In a bivariate context, we consider ill-posed inverse problems with incomplete theoretical and data information. We demonstrate the use of information theoretic methods for information recovery for a range of under-identified choice problems with more unknowns than data points. © 2007 Elsevier B.V. All rights reserved.

REGINN is an algorithm of inexact Newton type for the regularization of nonlinear ill-posed problems Inverse Problems 15 (1999), pp. 309-327]. In the present article convergence is shown under weak smoothness assumptions (source conditions). Moreover, convergence rates are established. Some computational illustrations support the theoretical results.

Ill-posed inverse problem is commonly existed in signal processing such as image reconstruction from projection, parameter estimation on electromagnetic field, and path optimization in IP network. Usually, the solution of an inverse problem is unstable, not unique or does not exit. Traditional approach to solve this problem is to estimate the solution by optimizing a regularized objective funct...

In voting rights cases, judges often infer unobservable individual vote choices from election data aggregated at the precinct level. That is, one must solve an ill-posed inverse problem to obtain the critical information used in these cases. The ill-posed nature of the problem means that traditional frequentist and Bayesian approaches cannot be employed without first imposing a range of assumpt...

We investigate the applicability of integral invariants as geometrical shape descriptors in the context of ill-posed inverse problems. We propose the use of a Tikhonov functional, where the penalty term is based on the difference of integral invariants. As a case example, we consider the problem of inverting the Radon transform of an object with only limited angular data available. We approxima...

Electrical capacitance tomography (ECT) technology has the softfield nature and the ill-posed problems. To solve the problem of low imaging quality by standard Tikhonov regularization, a wavelet fusion algorithm based on Tikhonov regularization is proposed in this paper. Firstly, Tikhonov regularization method is used to solve ill-posed characteristic of system inverse problem, then the initial...

Formulating a statistical inverse problem as one of inference in a Bayesian model has great appeal, notably for what this brings in terms of coherence, the interpretability of regularisation penalties, the integration of all uncertainties, and the principled way in which the set-up can be elaborated to encompass broader features of the context, such as measurement error, indirect observation, e...

Local regularization methods for ill-posed linear Volterra equations have been shown to be efficient regularization procedures preserving the causal structure of the Volterra problem and allowing for sequential solution methods. However questions posed recently in Ring and Prix (2000 Inverse Problems 16 619–34) raise doubts as to whether such methods are convergent for problems which are more t...