Regularized iterative and non-iterative procedures for object restoration from experimental data

A regularized algorithm for the recovery of band-limited signals from noisy data is described. The regularization is characterized by a single parameter. Iterative and non-iterative implementations of the algorithm are shown to have useful properties, the former offering the advantage of flexibility and the latter a potential for rapid data processing. Comparative results, using experimental data obtained in laser anemometry studies with a photon correlator, are presented both with and without regularization. © 1983 Taylor & Francis Ltd.

Regularized iterative and noniterative procedures for object restoration in the presence of noise :an error analysis

An analysis is carried out, using the prolate spheroidal wave functions, of certain regularized iterative and noniterative methods previously proposed for the achievement of object restoration (or, equivalently, spectral extrapolation) from noisy image data. The ill-posedness inherent in the problem is treated by means of a regularization parameter, and the analysis shows explicitly how the deleterious effects of the noise are then contained. The error in the object estimate is also assessed, and it is shown that the optimal choice for the regularization parameter depends on the signal-to-noise ratio. Numerical examples are used to demonstrate the performance of both unregularized and regularized procedures and also to show how, in the unregularized case, artefacts can be generated from pure noise. Finally, the relative error in the estimate is calculated as a function of the degree of superresolution demanded for reconstruction problems characterized by low space–bandwidth products.

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.

Object Restoration Beyond the Rayleigh Limit in the Presence of Noise

info:eu-repo/semantics/published

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.

Cellular immune responses in human immunodeficiency virus (HIV)-1-infected children: Is immune restoration by highly active anti-retroviral therapy comparable to non-progression?

The objective of this study was to investigate whether the restored immune functions of vertically human immunodeficiency virus (HIV)-infected children who were severely immunodeficient before the initiation of highly active anti-retroviral therapy (HAART) are comparable to those of untreated slow progressors. We therefore assessed T cell proliferation and cytokine [interferon (IFN)-γ, interleukin (IL)-5 and IL-13] secretions after mitogen, recall antigens and HIV-1-specific stimulation in 12 untreated slow progressors, 16 untreated progressors and 18 treated patients. Treated children were profoundly immunodeficient before the initiation of HAART and had long-lasting suppression of viral replication on treatment. We demonstrated that slow progressors are characterized not only by the preservation of HIV-1-specific lymphoproliferative responses but also by the fact that these responses are clearly T helper type 1 (Th1)-polarized. Children on HAART had proliferative responses to HIV-1 p24 antigen, purified protein derivative (PPD) and tetanus antigen similar to slow progressors and higher than those of progressors. However, in contrast to slow progressors, most treated children exhibited a release of Th2 cytokines accompanying the IFN-γ secretion in response to the HIV-1 p24 antigen. Moreover, despite higher proliferative responses to phytohaemagglutinin (PHA) than the two groups of untreated children, treated children had lower levels of IFN-γ secretion in response to PHA than slow progressors. These data show that in severely immunodeficient vertically HIV-infected children, a long-lasting HAART allows recovering lymphoproliferative responses similar to untreated slow progressors. However, alterations in IFN-γ secretion in response to the mitogen PHA persisted, and their cytokine release after HIV-specific stimulation was biased towards a Th2 response. © 2011 The Authors. Clinical and Experimental Immunology © 2011 British Society for Immunology.

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

A note on the restoration of optical objects

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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.