Superresolution and number of degrees of freedom in inverse diffraction with subwavelength sources

info:eu-repo/semantics/published

Number of degrees of freedom in inverse diffraction

The problem of inverse diffraction from plane to plane is considered in the case where a finite aperture exists in the boundary plane. Singular values and singular functions for the problem are introduced, and the number of degrees of freedom is defined in terms of the distribution of the singular values. Numerical computations are presented for the one-dimensional problem, and it is shown that the effect of evanescent waves disappears at a distance of approximately one wavelength from the boundary plane, even when the dimension of the slit is comparable with the wavelength of the diffracted field. © 1983 Taylor & Francis Group, LLC.

Stability and Resolution in Electromagnetic Inverse Scattering - Part I

info:eu-repo/semantics/published

Iterative inversion of experimental data in weighted spaces

We present iterative algorithms for solving linear inverse problems with discrete data and compare their performances with the method of singular function expansion, in view of applications in optical imaging and particle sizing.

Positive regularised solutions in electromagnetic inverse scattering

Fredholm integral equations of the first kind are the mathematical model common to several electromagnetic, optical and acoustical inverse scattering problems. In most of these problems the solution must be positive in order to satisfy physical plausibility. We consider ill-posed deconvolution problems and investigate several linear regularization algorithms which provide positive approximate solutions at least in the absence of errors on the data.

Applied Inverse Problems in Optics

info:eu-repo/semantics/published

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

info:eu-repo/semantics/published

Extraction of polydispersity information in photon correlation spectroscopy

info:eu-repo/semantics/published

Particle size distributions from Fraunhofer diffraction

info:eu-repo/semantics/published

Particle sizing by inversion of extinction data

info:eu-repo/semantics/published

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

info:eu-repo/semantics/published

LPS-binding protein and IL-6 Mark paradoxical tuberculosis immune reconstitution inflammatory syndrome in HIV patients

Background: Tuberculosis-associated immune reconstitution inflammatory syndrome (TB-IRIS) remains a poorly understood complication in HIV-TB co-infected patients initiating antiretroviral therapy (ART). The role of the innate immune system in TB-IRIS is becoming increasingly apparent, however the potential involvement in TB-IRIS of a leaky gut and proteins that interfere with TLR stimulation by binding PAMPs has not been investigated before. Here we aimed to investigate the innate nature of the cytokine response in TB-IRIS and to identify novel potential biomarkers. Methods: From a large prospective cohort of HIV-TB co-infected patients receiving TB treatment, we compared 40 patients who developed TB-IRIS during the first month of ART with 40 patients matched for age, sex and baseline CD4 count who did not. We analyzed plasma levels of lipopolysaccharide (LPS)-binding protein (LBP), LPS, sCD14, endotoxin-core antibody, intestinal fatty acid-binding protein (I-FABP) and 18 pro-and anti-inflammatory cytokines before and during ART. Results: We observed lower baseline levels of IL-6 (p = 0.041), GCSF (p = 0.036) and LBP (p = 0.016) in TB-IRIS patients. At IRIS event, we detected higher levels of LBP, IL-1RA, IL-4, IL-6, IL-7, IL-8, G-CSF (p ≤ 0.032) and lower I-FABP levels (p = 0.013) compared to HIV-TB co-infected controls. Only IL-6 showed an independent effect in multivariate models containing significant cytokines from pre-ART (p = 0.039) and during TB-IRIS (p = 0.034). Conclusion: We report pre-ART IL-6 and LBP levels as well as IL-6, LBP and I-FABP levels during IRIS-event as potential biomarkers in TB-IRIS. Our results show no evidence of the possible contribution of a leaky gut to TB-IRIS and indicate that IL-6 holds a distinct role in the disturbed innate cytokine profile before and during TB-IRIS. Future clinical studies should investigate the importance and clinical relevance of these markers for the diagnosis and treatment of TB-IRIS. Copyright: © 2013 Goovaerts et al.