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

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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.

The methyl-CpG-binding protein MECP2 is required for prostate cancer cell growth.

The incidence of prostate cancer is increasing in western countries because of population aging. Prostate cancer begins as an androgen-dependent disease, but it can become androgen independent at a later stage or in tumors recurring after an antihormonal treatment. Although many genetic events have been described to be involved in androgen-dependent and/or -independent prostate cancer growth, little is known about the contribution of epigenetic events. Here we have examined the possibility that the methyl-CpG-binding protein MECP2 might play a role in controlling the growth of prostate cancer cells. Inhibition of MECP2 expression by stable short hairpin RNA stopped the growth of both normal and cancer human prostate cells. In addition, ectopic expression of the MECP2 conferred a growth advantage to human prostate cancer cells. More importantly, this expression allowed androgen-dependent cells to grow independently of androgen stimulation and to retain tumorigenic properties in androgen-depleted conditions. Analysis of signaling pathways showed that this effect is independent of androgen receptor signaling. Instead, MECP2 appears to act by maintaining a constant c-myc level during antihormonal treatment. We further show that MECP2-expressing cells possess a functional p53 pathway and are still responsive to chemotherapeutic drugs.

Ets-1 p27: A novel Ets-1 isoform with dominant-negative effects on the transcriptional properties and the subcellular localization of Ets-1 p51

The transcription factor Ets-1 is implicated in various physiological processes and invasive pathologies. We identified a novel variant of ets-1, ets-1Delta(III-VI), resulting from the alternative splicing of exons III to VI. This variant encodes a 27 kDa isoform, named Ets-1 p27. Ets-1 p27 lacks the threonine-38 residue, the Pointed domain and the transactivation domain, all of which are required for the transactivation of Ets-1 target genes. Both inhibitory domains surrounding the DNA-binding domain are conserved, suggesting that Ets-1 p27, like the full-length Ets-1 p51 isoform, is autoinhibited for DNA binding. We showed that Ets-1 p27 binds DNA in the same way as Ets-1 p51 does and that it acts both at a transcriptional and a subcellular localization level, thereby constituting a dual-acting dominant negative of Ets-1 p51. Ets-1 p27 blocks Ets-1 p51-mediated transactivation of target genes and induces the translocation of Ets-1 p51 from the nucleus to the cytoplasm. Furthermore, Ets-1 p27 overexpression represses the tumor properties of MDA-MB-231 mammary carcinoma cells in correlation with the known implication of Ets-1 in various cellular mechanisms. Thus the dual-acting dominant-negative function of Ets-1 p27 gives to the Ets-1 p27/Ets-1 p51 ratio a determining effect on cell fate.

Ectopic expression of the Ets transcription factor ER81 in transgenic mouse mammary gland enhances both urokinase plasminogen activator and stromelysin-1 transcription

The PEA3 group members PEA3, ER81 and ERM, which are highly conserved transcription factors from the Ets family, are over-expressed in metastatic mammary tumors. In the current study, we present the characterization of a transgenic mouse strain which over-expresses ER81 in the mammary gland via the long terminal repeat of the mouse mammary tumor virus (LTR-MMTV). Although six genotypically positive transgenic lines were identified, only one expressed the ectopic transcript with an exclusive expression in the lactating and late-pregnancy (18th day) mammary glands. No mammary tumor or mammary deregulation appeared after 2 years of ectopic ER81 expression following lactation. We then sought to identify ER81 target genes, and the urokinase plasminogen activator (uPA) and the stromelysin-1, two enzymes involved in extracellular matrix degradation, were found to be transcriptionally upregulated in lactating mammary glands over-expressing ER81. Since these enzymes are involved in metastasis, this murine model could be further used to enhance mammary cancer metastatic process by crossing these animals with mice carrying non-metastatic mammary tumors. We thus created a transgenic mouse model permitting the over-expression of a functionally active Ets transcription factor in the mammary gland without perturbing its development.

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.