1,354,352 research outputs found
Legendre quadrature for the discretization of 1D radiating panels
No full textIn [A. Capozzoli, C. Curcio, A. Liseno, MMS, Pizzo Calabro, Italy, 2022], the problem of modeling a source/scatterer using an equivalent radiator has been addressed and an approach has been given and numerically assessed. Once dimensioned the radiating panel, a practical implementation can be provided by a non-uniform array. The element positions should be chosen so that the array is capable to approximate, with an adequate accuracy, the fields radiated by the equivalent radiator. Here, the array element positioning is performed by exploiting a quadrature rule which takes into account that the singular functions supported on the region of interest associated to the most significant singular values of the radiation operator are related to those supported on the equivalent panel by a radiation integral. The quadrature rule enables also to choose a set of weights which are essential in the definition of the element excitation coefficients from the knowledge of the source distribution on the equivalent panel. For simplicity, a one-dimensional problem with a Legendre quadrature rule is considered. The approach is numerically assessed by checking the capability of the array to radiate, with a satisfactory degree of accuracy, the singular functions associated to the region of interest
Imaging of voids by means of a physical-optics-based shape-reconstruction algorithm
No full textWe analyze the performance of a shape-reconstruction algorithm for the retrieval of voids starting from the electromagnetic scattered field. Such an algorithm exploits the physical optics (PO) approximation to obtain a linear unknown-data relationship and performs inversions by means of the singular-value-decomposition approach. In the case of voids, in addition to a geometrical optics reflection, the presence of the lateral wave phenomenon must be considered. We analyze the effect of the presence of lateral waves on the reconstructions. For the sake of shape reconstruction, we can regard the PO algorithm as one of assuming the electric and magnetic field on the illuminated side as constant in amplitude and linear in phase, as far as the dependence on the frequency is concerned. Therefore we analyze how much the lateral wave phenomenon impairs such an assumption, and we show inversions for both one single and two circular voids, for different values of the background permittivity
A novel optimization approach to forest height reconstruction from multi-baseline data
No full textThe paper deals with the problem of reconstructing the
height of forests from polarimetric/multi-baseline SAR data. The
approach consists of optimizing an objective functional defined
as the distance between the measured data and the data predicted
by the model at the actual estimate of the unknowns.
We indicate the role of global optimization on the performance of
the forest height reconstruction algorithm. As global optimizer, a
multilevel single-linkage method, which incorporates a local
optimization into the global search, is exploited, thus offering
computational efficiency and reliability. The performance of the
method are illustrated against numerically simulated data
Improving a shape reconstruction algorithm with thresholds and multi-view data
No full textThis paper deals with the reconstruction of the shape of unknown perfectly conducting objects from the knowledge of the scattered electric far field in a two-dimensional geometry. By adopting the Kirchhoff approximation, the problem is cast as a linear inverse one and is solved by resorting to the Singular Value Decomposition (SVD) approach. The finiteness of the available data along with the presence of the noise make undesired features on the reconstructed image arise. We here give some criteria for the choice of a threshold to cut them out from the reconstructions. Furthermore, we illustrate the processing of multi-view data
Imaging perfectly conducting objects as support of induced currents: Kirchhoff approximation and frequency diversity
No full textThe problem of determining the shape of perfectly conducting objects from knowledge of the scattered electric field is considered. The formulation of the problem accommodates the nature of the distribution of the induced surface current density. Thus, as the unknown representing the object’s contour, a single layer distribution is chosen so that the contour of the scatterer is described by its support. The nonlinear unknown-data mapping is then linearized by means of the Kirchhoff approximation, and the problem is recast as the inversion of a linear operator acting on a distribution space. An extension of the singular value decomposition approach to solve the linearized problem is provided and numerical results are presented
Impossibility of recovering a scatterer’s shape by the first version of the “linear sampling” method
No full textThe version of the “linear sampling” method introduced in D. Colton, A. Kirsch, Inverse Problems, 12, 383, 1996, is analyzed.
It consists into the attempt to recover a scatterer's contour by determining an indicator function from the knowledge of the scattered far field data. In particular, the indicator function is determined following the solution of a certain far field equation.
We show that the far field equation to solve does not have (almost anywhere) a solution for two classes of objects: Perfectly conducting cylinders and homogeneous dielectric cylinders having circular cross section. It thus follows that the indicator function is “infinite” (almost) everywhere both inside and outside the scatterer and, consequently, does not represent the shape of the object
In-depth resolution for a strip source in the Fresnel zone
No full textThe problem of determining the achievable resolution limits in the reconstruction of a current distribution is considered. The analysis refers to the one-dimensional, scalar case of a rectilinear, bounded electric current distribution when data are collected by measurement of the radiated field over a finite rectilinear observation domain located in the Fresnel zone, orthogonal and centered with respect to the source. The investigation is carried out by means of analytical singular-value decomposition of the radiation operator connecting data and unknown, which is made possible by the introduction of suitable scalar products in both the unknown and data spaces. This strategy permits the use of the results concerning prolate spheroidal wave functions described by B. R. Frieden [Progress in Optics Vol. IX, E. Wolf, ed. (North-Holland, Amsterdam 1971), p. 311.] For values of the space–bandwidth product much larger than 1, the steplike behavior of the singular values reveals that the inverse problem is severely ill posed. This, in turn, makes it mandatory to use regularization to obtain a stable solution and suggests a regularization scheme based on a truncated singular-value decomposition. The task of determining the depth-resolving power is accomplished with resort to Rayleigh’s criterion, and the effect of the geometrical parameters of the measurement configuration is also discussed
"Ricostruzione di forme d'onda di oggetti fortemente diffusori attraverso modelli distyribuzionali"
No full textShape reconstruction from PO multifrequency scattered fields via the singular value decomposition approach
No full textThis paper deals with the problem of determining the shape of unknown perfectly conducting infinitely long cylinders, starting from the knowledge of the scattered electric far field under the incidence of plane waves with a fixed angle of incidence and varying frequency. The problem is formulated as a nonlinear inverse one by searching for a compact support distribution accounting for the objects contour. The nonlinear unknown to data mapping is then linearized by means of the Kirchhoff approximation, which reduces it into a Fourier transform relationship. Then, the Fourier transform inversion from incomplete data is dealt with by means of the singular value decomposition (SVD) approach and the features of the reconstructable unknowns are investigated. Finally, numerical results confirm the performed analysi
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