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.

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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Superresolution in linear inverse problems

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Multicenter randomized trial of dacarbazine alone or in combination with two different doses and schedules of interferon alfa-2a in the treatment of advanced melanoma

Purpose: Some phase II studies have suggested that the combination of interferons (IFNs) with dacarbazine (DTIC) in the treatment of malignant melanoma (MM) increases the antitumor activity of DTIC alone. In an attempt to confirm this hypothesis, a randomized study was performed with the further intent of observing whether low doses of recombinant interferon alfa-2a (rIFNα2a) could be as effective as intermediate doses. Patients and Methods: Two hundred sixty-six patients were randomized onto three different treatment arms: DTIC 800 mg/m 2 intravenously (IV) days 1 and 21; DTIC plus rIFNα2a 9 mIU intramuscularly (IM) daily; and DTIC plus rIFNα2a 3 mIU IM three times per week. Major prognostic factors were well balanced among the three arms. Chemotherapy was administered for a maximum of eight cycles. After 6 months of therapy, rIFNα2a was continued until disease progression at 3 mIU three times per week in responding patients who had received the combined treatment. Results: The percentage of objective responses did not differ among the three groups (20%, 28%, and 23%, respectively), although a significant prolongation of response duration was observed when rIFNα2a was added to DTIC (2.6 v 8.4 v 5.5 months, respectively). However, this improvement in response duration did not translate into an amelioration of overall survival. The addition of rIFNα2a led to the onset of flu-like syndrome, but in no case was it necessary to withdraw the treatment program and no toxic deaths or life-threatening toxicities were reported. Conclusion: In this study, rIFNα2a significantly prolonged response duration, whereas no effects on response rate and survival were observed; rIFNα2a 3 mIU appeared to be equally effective and better tolerated than 9 mIU.