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...

We present an error analysis for the numerical diierentiation of noisy data via smoothing cubic splines. Our treatment is elementary enough to be included in a course on numerical analysis. Still, it accounts for all numerical problems that arise in the solution of much more complex ill-posed inverse problems.

In this work we present and analyze a Kaczmarz version of the iterative regularization scheme REGINN-Landweber for nonlinear ill-posed problems in Banach spaces [Jin, Inverse Problems 28(2012), 065002]. Kaczmarz methods are designed for problems which split into smaller subproblems which are then processed cyclically during each iteration step. Under standard assumptions on the Banach space and...

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.

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.

The focus of this paper is on conditional stability estimates for illposed inverse problems in partial differential equations. Conditional stability estimates have been obtained in the literature by a couple different methods. In this paper we propose a method called interpolation method, which is based on interpolation in variable Hilbert scales. We are going to work out the theoretical backgr...

Environment measurement is an important issue for various applications including household robots. Pulse radars are promising candidates in a near future. Estimating target shapes using waveform data, which we obtain by scanning an omni-directional antenna, is known as one of ill-posed inverse problems. Parametric methods such as Model-fitting method have problems concerning calculation time an...

Inverse heat conduction problems, which are one of the most important groups of problems, are often ill-posed and complicated problems, and their optimization process has lots of local extrema. This paper provides a novel computational procedure based on finite differences method and league championship algorithm to solve a one-dimensional inverse heat conduction problem. At the beginning, we u...