Ill-posed Inverse Problems and Logarithmic Continuity in Electromagnetics

info:eu-repo/semantics/published

Health networks: Actors, professional relationships, and controversies

In recent years international policies have aimed to stimulate the use of information and communication technologies (ICT) in the field of health care. Belgium has also been affected by these developments and, for example, health electronic regional networks ("HNs") are established. Thanks to a qualitative case study we have explored the implementation of such innovations (HN) to better understand how health professionals collaborate through the HN and how the HN affect their relationships. Within the HNs studied a common good unites the actors: the continuity of care for a better quality of care. However behind this objective of continuity of care other individual motivations emerge. Some controversies need also to be resolved in order to achieve cooperative relationships. HNs have notably to take national developments into account. These developments raise the question of the control of medical knowledge and medical practice. Professional issues, and not only practical changes, are involved in these innovations. © 2008 The authors and IOS Press. All rights reserved.

On the problems of object restoration and image extrapolation in optics

In this paper we consider the problems of object restoration and image extrapolation, according to the regularization theory of improperly posed problems. In order to take into account the stochastic nature of the noise and to introduce the main concepts of information theory, great attention is devoted to the probabilistic methods of regularization. The kind of the restored continuity is investigated in detail; in particular we prove that, while the image extrapolation presents a Hölder type stability, the object restoration has only a logarithmic continuity. © 1979 American Institute of Physics.

Resolution beyond the diffraction limit for regularized object restoration

We propose a new formulation of Miller's regularization theory, which is particularly suitable for object restoration problems. By means of simple geometrical arguments, we obtain upper and lower bounds for the errors on regularized solutions. This leads to distinguish between ' Holder continuity ' which is quite good for practical computations and ` logarithmic continuity ' which is very poor. However, in the latter case, one can reconstruct local weighted averages of the solution. This procedure allows for precise valuations of the resolution attainable in a given problem. Numerical computations, made for object restoration beyond the diffraction limit in Fourier optics, show that, when logarithmic continuity holds, the resolution is practically independent of the data noise level. © 1980 Taylor & Francis Group, LLC.

Stability Problems in Inverse Diffraction

Inverse diffraction consists in determining the field distribution on a boundary surface from the knowledge of the distribution on a surface situated within the domain where the wave propagates. This problem is a good example for illustrating the use of least-squares methods (also called regularization methods) for solving linear ill-posed inverse problem. We focus on obtaining error bounds For regularized solutions and show that the stability of the restored field far from the boundary surface is quite satisfactory: the error is proportional to ∊(ðŗ‚ ≃ 1) ,ðŗœ being the error in the data (Hölder continuity). However, the error in the restored field on the boundary surface is only proportional to an inverse power of │In∊│ (logarithmic continuity). Such a poor continuity implies some limitations on the resolution which is achievable in practice. In this case, the resolution limit is seen to be about half of the wavelength. Copyright © 1981 by The Institute of Electrical and Electronics Engineers, Inc.