Applied Inverse Problems in Optics

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Inversion of light scattering data by singular system analysis

We consider the problem of inverting experimental data obtained in light scattering experiments described by linear theories. We discuss applications to particle sizing and we describe fast and easy-to-implement algorithms which permit the extraction, from noisy measurements, of reliable information about the particle size distribution. © 1987, SPIE.

The Use of Singular Systems and other Inversion Methods in Weighted L2- spaces

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Extraction of polydispersity information in photon correlation spectroscopy

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Particle size distributions from Fraunhofer diffraction

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Particle sizing by inversion of extinction data

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Linear inverse problems with discrete data: II. Stability and regularization

For pt.I. see ibid. vol.1, p.301 (1985). In the first part of this work a general definition of an inverse problem with discrete data has been given and an analysis in terms of singular systems has been performed. The problem of the numerical stability of the solution, which in that paper was only briefly discussed, is the main topic of this second part. When the condition number of the problem is too large, a small error on the data can produce an extremely large error on the generalised solution, which therefore has no physical meaning. The authors review most of the methods which have been developed for overcoming this difficulty, including numerical filtering, Tikhonov regularisation, iterative methods, the Backus-Gilbert method and so on. Regularisation methods for the stable approximation of generalised solutions obtained through minimisation of suitable seminorms (C-generalised solutions), such as the method of Phillips (1962), are also considered.

Super-resolution in confocal scanning microscopy: II :The incoherent case

For pt.I see ibid. vol.3, p.195 (1987). The authors have shown that the resolution of a confocal scanning microscope can be improved by recording the full image at each scanning point and then inverting the data. These analyses were restricted to the case of coherent illumination. They investigate, along similar lines, the incoherent case, which applies to fluorescence microscopy. They investigate the one-dimensional and two-dimensional square-pupil problems and they prove, by means of numerical computations of the singular value spectrum and of the impulse response function, that for a signal-to-noise ratio of, say 10%, it is possible to obtain an improvement of approximately 60% in resolution with respect to the conventional incoherent light confocal microscope. This represents a working bandwidth of 3.5 times the Rayleigh limit.

SVD for linear inverse problems

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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.

Immunological Signatures Identifying Different Stages of Latent Mycobacterium tuberculosis Infection and Discriminating Latent from Active Tuberculosis in Humans

Objectives: One third of the world population is considered latently infected with Mycobacterium tuberculosis(LTBI) and sterilizing this reservoir of bacteria that may reactivate is required for tuberculosis (TB) elimination. Thegroup of individuals with LTBI is heterogeneous with some of them being more at risk to develop TB disease thanothers. Improved diagnosis of subjects with LTBI is needed, allowing to differentiate subjects with LTBI from thosewith active TB, and to select among LTBI subjects those who are more at risk to develop active TB. We havecharacterized at the cellular level both the quantitative and qualitative T cell responses to different mycobacterialantigens in selected populations of infected subjects in order to identify new biomarkers that could help to identify M.tuberculosis-infected subjects and to stratify them in risk groups for reactivation of the infection.Methods: Lymphoblast frequencies and cytokine production (IFN-γ, TNF-α, IL-2) among CD4+ and CD8+ T cellswere analyzed by flow cytometry after in vitro stimulation with the latency antigen heparin-binding haemagglutinin(HBHA) or early-secreted antigen Target-6 (ESAT-6) of peripheral blood mononuclear cells from clinically wellcharacterized M. tuberculosis-infected humans (28 LTBI, 22 TB disease,12 controls). The LTBI group definedaccording to the Center for Disease Control guidelines was subdivided into QuantiFERON-TB Gold in-Tube (QFT)positive and negative subgroups.Results: Similar to TB patients, QFT+ LTBI subjects had higher proportions of HBHA-induced TNF-αsingle+ CD4+lymphocytes than QFT- LTBI subjects (p<0.05). Compared to LTBI subjects, TB patients had higher frequencies ofESAT-6-induced CD8+ lymphoblasts (p<0.001), higher proportions of ESAT-6-induced IFN-γ+TNF-α+ CD4+ Tlymphocytes (p<0.05), and lower proportions of HBHA-induced IFN-γ+TNF-α+IL-2+ (p<0.05) CD4+ T lymphocytes.Conclusions: These data provide new biomarkers to discriminate active TB from LTBI, and more interestingly,help to identify LTBI subjects with increased likelihood to develop TB disease.

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

Expression of galectin-3 in the tumor immune response in colon cancer.

The role of tumor-associated macrophages (TAMs) is controversial. Although most studies on different cancer types associate them with a poorer prognosis, interestingly in colon cancer, most articles indicate that TAMs prevent tumor development; patients with high TAMs have better prognosis and survival rate. M1-polarized macrophages produce high level of tumor necrosis factor-alpha, interleukin-1 beta or reactive oxygen species, which can effectively kill susceptible tumor cells. In contrast, M2-polarized macrophages can secrete different factors that promote tumor cell growth and survival or favor angiogenesis and tissue invasion. Considering the beneficial role of TAMs in colon cancer, we speculated that they may not display the M2 polarization commonly observed in tumor microenvironment, but rather develop M1 properties. Therefore, we used an in vitro model to analyze the effects of supernatants from M1-polarized macrophages on DLD-1 colon cancer cells. Our data indicate that the conditioned medium from LPS-activated macrophages (CM-LAM) contains a high level of granulocyte-macrophage colony-stimulating factor, interleukins-1 beta, -6, -8 and tumor necrosis factor-alpha, and that it exerts a marked growth inhibitory activity on DLD-1 cells. Prolonged exposure to CM-LAM results in cell death by apoptosis. Such exposure to CM-LAM leads to the modulation of gal-3 expression: we observed a marked downregulation of gal-3 mRNA and protein expression following CM-LAM treatment. We also describe that the knockdown of gal-3 sensitizes DLD-1 cells to CM-LAM. These data suggest an involvement of gal-3 in the response of colon cancer cells to proinflammatory stimuli, such as the conditioned medium from activated macrophages.

Développement ontogénique des lymphocytes B chez la souris et inactivation de jeunes lymphocytes B par un antigène

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