PIANA , Michele

The problem of determining the shape of an object from far-field data is considered. We present a method, originally formulated in Ref. 1 and furtherly modified in Ref. 3, for the solution of this ill-posed nonlinear inverse problem whose main features are: • the method is exact, that is no low- or high-frequency approximation is considered; •...

Bremsstrahlung radiation coming from the solar atmosphere is linked to the distribution function of electrons in the solar plasma through a Volterra equation of the first kind. We have assumed the Bethe-Heitler approximation for the bremsstrahlung cross section and we have applied the SVD method to the integral equation with discrete data....

The problem of determining the shape of a two-dimensional inhomogeneous orthotropic scatterer from far-field data is considered. In particular, by using integral equation techniques we prove that the support of the scatterer is uniquely determined if the far-field pattern is known for all incident directions. We point out that this uniqueness...

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This paper studies the regularization of constrained Maximum Likelihood iterative algorithms applied to incompatible ill-posed linear inverse problems. Specifically we introduce a novel stopping rule which defines a regularization algorithm for the Iterative Space Reconstruction Algorithm in the case of Least-Squares minimization. Further we...

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In two previous papers in this journal we presented a simple method for determining the support of a scattering object from noisy far-field data for transverse magnetic polarized electromagnetic waves. This method was based on the solution of a linear integral equation of the first kind with the mathematical analysis being based on an...

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The projected Landweber method is an iterative method for solving constrained least-squares problems when the constraints are expressed in terms of a convex and closed set C. The convergence properties of the method have been recently investigated. Moreover, it has important applications to many problems of signal processing and image...

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In recent publications the problem of deconvolving multiple images of the same object was considered, and the fact that this problem can be well posed in the sense of distributions was stressed. Here we point out that the problem is still ill posed in spaces of square-integrable functions, and we discuss in what cases the use of multiple images...

Physical optics is an asymptotic scattering regime where the wavelength of the incident field is much smaller than the linear dimensions of the scatterer. In such conditions, the inverse scattering problem of determining the object profile from measurements of the far-field pattern can be formulated in terms of a linear integral equation of the...

In suitable conditions on the radiation source the synchrotron process can be described by a Fredholm integral equation whose integral kernel is expressed in terms of a modified Bessel function of the second kind. We present a completely general solution of this equation. We point out that the linear inverse problem of determining the electron...

The most direct representation of the measurements provided by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) is a set of Fourier components of the X-ray radiation sam- pled at discrete points of the spatial frequency plane, the so called visibilities. Here we review methods for the reconstruction of X-ray and elec- tron maps...

The instability properties of bremsstrahlung spectrum inversion to yield source electron spectra in flares are examined in terms of singular value decomposition (SVD) for the cases of thin- and thick-target models for different bremsstrahlung cross-sections. It is shown that, for the Kramers and Bethe-Heitler cross-sections, analytic...

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A two-step reconstruction scheme is introduced to solve fixed frequency inverse scattering problems in Born approximation conditions. The aim of the approach is to achieve super-resolution effects by constraining the inversion method to exploit some a priori knowledge on the scatterer. Therefore, the first step is to apply the linear sampling...

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