A new inversion procedure for confocal scanning microscopy and other bandlimited signal processing problems

We find a simple analytic expression for the inverse of an infinite matrix related to the problem of data reduction in confocal scanning microscopy and other band-limited signal processing problems. Potential applications of this result to practical problems are outlined. The matrix arises from a sampling expansion approach to the integral equation.

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.

La formation discursive eurorégionale. Articulation et approche sémantique d’un corpus multilingue

L’objectif de cet article est double :il s’agit, d’une part, de présenter un nouveau corpus permettant d’envisager le phénomène émergent de la communication transfrontalière en Europe et, d’autre part, de formuler trois questionnements utiles au cadrage de son analyse sémantique. À partir du corpus eurorégional – multilingue et multigenre - nous posons les questions de la dispersion des discours en ligne, de l’hétérogénéité des données et de la contextualisation de l’analyse. Notre démarche consiste à construire progressivement un modèle d’analyse adapté à l’appréhension, tantôt automatique et tantôt manuelle, de la diversité des textes. Enfin, nous proposons d’illustrer la démarche en l’appliquant à la mobilité, observable récurrent du corpus.

Restoration of optical objects using regularization

Using the regularization theory for improperly posed problems, we discuss object restoration beyond the diffraction limit in the presence of noise. Only the case of one-dimensional coherent objects is considered. We focus attention n the estimation of the error on the restored objects, and we show that, in most realistic cases, it is at best proportional to an inverse power of

Evaluation de DI-fusion: Le dépôt officiel de l'ULB

info:eu-repo/semantics/published

Superresolution in linear inverse problems

info:eu-repo/semantics/published

Signal restoration from band-pass filtered data

The restoration problem for a band-pass linear system is examined in the case the input signal is weighted by a profile function. The singular system is evaluated analytically for three different forms of the profile function. An example of restoration process is presented.