A quadratic model for inverse profiling: the one-dimensional case

Brancaccio, Adriana; Pascazio, Vito; Pierri, Rocco

doi:10.1163/156939395x00875

Cited by 38 publications

(19 citation statements)

References 14 publications

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“…As well known, such an equation can be solved iteratively, thus obtaining the so-called Neumann series [4] (9) whose terms are (10) We stress that to stop (9) to the first term is connected to the usual assumption of smallness of the norm of the function, holding in the weak scattering case. This sets a limit to the dimensions of the scatterer with respect to the wavelength and the norm of the contrast function.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…QUADRATIC APPROACH A better approximation of the scattered field is certainly available if the Neumann series (11) of is stopped [9] to the second term, so obtaining the sum of two operators (17) where is the previously defined linear operator and is a quadratic one.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…The method we present is based on a quadratic approximation [9] of the operator linking the unknown permittivity function and the scattered electric field, whose complex samples are the data of the problem. Such an analysis is preliminary to accurately approach the general nonlinear problem because it makes it possible not only to reconstruct a larger class of dielectric profiles with respect to the linear method, but to understand which factors affect critically the reliability of the solution algorithm with respect to the occurrence of false solutions.…”

Section: Introductionmentioning

confidence: 99%

“…The most common approach to solve the problem consists in linearizing it [7], [8], but this approximation introduces in the inversion serious limitations concerning the dimension of the scatterer (with respect to the wavelength of the incident radiation), the maximum value of permittivity and the spatial variability of the dielectric profile [9]- [12], as we will see in the following. Iterative methods (Born and distorted Born iterated methods [13], [14] and Newton-Kantorovich method [15], [16]) are based on the resolution of a sequence of linearized problems, but they converge only under particular conditions.…”

Section: Introductionmentioning

confidence: 99%

“…We refer in this paper to a two-dimensional (2-D) geometry, thus extending the approach of [9] for the one-dimensional (1-D) case toward more realistic applications; moreover, in order to avoid unnecessary details from complicated spatial variations of the unknown functions and point out in a simple way the main features of the approach we are going to introduce, the reference situation of only angular dependence of the dielectric profiles is examined. Thus, we can immediately discuss the direct influence of the quadratic approach with respect to the attainable spatial resolution.…”

Section: Introductionmentioning

confidence: 99%

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Inverse scattering of dielectric cylinders by a second-order Born approximation

Pierri¹,

Leone²

1999

IEEE Trans. Geosci. Remote Sensing

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The inverse problem of the reconstruction of the permittivity profile of a dielectric cylinder from the knowledge of the scattered electric field is examined. The proposed method is based on a quadratic approximation of the nonlinear operator defining the scattered field. This choice overcomes the typical limitations of linear approaches and, due to the quadraticity of the operator involved, makes it possible to discuss and avoid the presence of local minima in the inversion procedure. The main features of the approach are shown for the simple case of dielectric cylinders with only angular dependence of permittivity, pointing out the higher sensitivity of the proposed approach with respect to fast varying profiles and the possibility to increase the spatial resolution when the number of available independent data are sufficiently larger than the number of unknowns.Index Terms-Dielectric profile reconstruction, electromagnetic scattering inverse problems, nonlinear inverse problems.

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Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Formulation Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Inverse scattering of dielectric cylinders by a second-order Born approximation

Pierri¹,

Leone²

1999

IEEE Trans. Geosci. Remote Sensing

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Recent advances in short-range microwave imaging in europe

Pastorino

1998

J. of Shanghai Univ.

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This paper reports the content of a lecture presented at the 1995 International Conference and Exhibition on Electronic Measurement and Instrumentation, held in Shanghai, China in 1995. The paper presents (thanks to the courtesy of several scientists) some of the most significant esults recently obtained in the field of short-range microwave imaging. The overview concerns the research activity carried out in Europe and is focused on microwave imaging for non-destructive testing, civil engineering, and scientific and medical applications. This type of imaging is characterized by a relatively short distance between the object to be detected and the probes.which is in general the starting point for microwaveimaging algorithms, is mathematically formulated. Then, the paper provides references to several significant imaging approaches so far proposed. For details of these approaches, the reader is referred to the numerous mentioned papers. Finally, a description of the research activity carried out in Europe is given and some very interesting results are shown.

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