1,721,054 research outputs found
Information content in inverse source with symmetry and support priors
No full textThis paper illustrates how inverse source problems are affected by certain symmetry and support priors concerning the source space. The study is developed for a prototype configuration where the field radiated by square integrable strip sources is observed in far-zone. Three symmetry priors are considered: the source is a priori known to be a real or Hermitian or even (resp. odd) function. Instead, as spatial priors we assume that the source support consists of a single or multiple disjoint domains. The role of the aforementioned priors is assessed against some metrics commonly used to characterise inverse source problems such as the number of degrees of freedom, the point-spread function and the âinformation contentâ measured through the Kolmogorov entropy
Resolution limits in inverse source problem for strip currents not in Fresnel zone
No full textThis paper deals with the classical question of estimating achievable resolution in terms of configuration parameters in inverse source problems. In particular, the study is developed for two-dimensional prototype geometry, where a strip source (magnetic or electric) is to be reconstructed from its radiated field observed over a bounded rectilinear domain parallel to the source. Resolution formulas are well known when the field is collected in the far field or in the Fresnel zone of the source. Here, the plan is to expand those results by removing the geometrical limitations due to the far field or Fresnel approximations. To this end, the involved radiation operators are recast as Fourier-type integral operators upon introducing suitable variable transformations. For magnetic sources, this allows one to find a closed-form approximation of the singular system and hence to estimate achievable resolution, the latter given as the main beam width of the point-spread function. Unfortunately, this does not happen for electric currents. In this case, the radiation operator is inverted by a weighted adjoint inversion method (a back-propagation-like method) that directly allows one to find an analytical expression of the point-spread function and hence of the resolution. The derived resolution formulas are the same for magnetic and electric currents; they clearly point out the role of geometrical parameters and coincide with the one pertaining to the Fresnel zone when the geometry verifies the Fresnel approximation. A few numerical examples are also enclosed to check the theory
Sensor Arrangement in Monostatic Subsurface Radar Imaging
No full textThis paper deals with microwave subsurface imaging achieved by inverting the linearized scattering operator. The focus is on the determination of a strategy for spatially sampling the data which allows to reduce the spatial data measurements and at the same time to keep the same achievable performance in the reconstructions. To this end, the measurement points are determined in order to approximate the point-spread function corresponding to the ideal continuous case (i.e., the case in which the data space is not sampled at all). For the sake of simplicity, the study is developed for a 2D scalar configuration. Also, the standard mono-static measurement arrangement is considered. However, in order to mimic a subsurface imaging scenario, a two-layered background medium is addressed. The main idea is to introduce suitable variable transformations which allow to express the point-spread functions as a Fourier-like transformation; this then provides insights for devising the sampling scheme. It is shown the resulting measurement spatial positions must be non-uniformly arranged across the measurement domain and their number can be much lower than the one provided by some commonly used literature sampling criteria
Near-Field Transverse Resolution in Planar Source Reconstructions
No full textThis paper deals with the classical question of estimating the achievable resolution in terms of the configuration parameters in inverse source problems. In particular, the study focuses on the case of a planar surface magnetic current which is to be reconstructed from near-field observed over a bounded rectangular aperture parallel to the source domain. Here, the plan is to work out a resolution estimation that precisely captures the spatially varying behaviour entailed by the near-field and aspect-limited configuration. To this end, the pertinent radiation operator is inverted by an adjoint inversion scheme (a backpropagation- like method) and the corresponding point-spread function is analytically estimated. Numerical examples show that the derived resolution estimation clearly points out the role of the geometrical parameters of the configuration and it is more accurate than other literature results
Inverse source of circumference geometries: SVD investigation based on fourier analysis
No full textThe role of the source geometry is investigated within the realm of inverse source problems. In order to examine the properties of the far zone radiation operator of some 2D curved sources its Singular Value Decomposition (SVD) is studied, either analytically, when possible, or numerically. This allows to evaluate the number of independent pieces of information, i.e., the number of degrees of freedom (NDF), of the source and to point out the set of far zone fields corresponding to stable solutions of the inverse problem. In particular, upper bounds for the NDF are obtained by exploiting Fourier series representations of the singular functions. Both curved (i.e., circumference and arc of circumference) and rectilinear geometries are considered, pointing out the role of limited angular observation domains. Moreover, in order to obtain some clues about the resolution achievable in the inverse source problem, a point-spread function analysis is performed. The latter reveals a spatially variant resolution for limited angular observation domains. The practical relevance of these results is highlighted with numerical examples of array diagnostics
Sampling approach for singular system computation of a radiation operator
No full textThe problem of computing the singular system of the radiation operator pertaining to the case of strip currents is dealt with. The associate eigenvalue problem involves a space-variant operator whose kernel is not band-limited. As a consequence, the sampling approach, which has been recently introduced for computing the eigenwavefronts of some band-limited linear space-invariant imaging systems, cannot be used as such. To overcome this drawback, it is shown that the kernel function can be recast as a varying band-limited function. This allows exploiting the pseudo-sampling series theory from which a sampling approximation of the kernel function is derived and eventually used to set the discrete eigenvalue problem. In particular, unlike the classical sampling approach, the sampling points turn out to be non-uniformly distributed. Some numerical examples are used to check the theory. It is shown that the most significant part of the singular system can be very accurately computed by using a number of samples slightly greater than the Shannon number
Inverse scattering in the presence of a reflecting plane
No full textThe role played by a reflecting plane embedded in the host medium in inverse scattering
problems is dealt with for a scalar two dimensional configuration. To accomplish such a task,
analytical arguments are developed to estimate the singular value decomposition (SVD) of the
relevant scattering operator. This allows us to gather quantitative measures of the information
that can be conveyed back from data to the unknown, to determine the so-called number of
degrees of freedom (NDF) and to estimate the achievable resolution. The analysis highlights that
the presence of reflections or scattering positively impacts the inverse scattering problem
A sampling strategy of the radiation operator in near-zone based on an asymptotic kernel
Full text linkIn this paper, we address the problem of discretizing the singular system of the radiation operator concerning the case of a magnetic strip current whose radiated field is observed in near-zone on a bounded line parallel to the source. This question has been already addressed in previous articles with the limitation that the extension of the observation domain does not overcome the source size. In this article, we remove such limitation, hence, we provide a discrete model that well approximates the singular values of the radiation operator in the case where the observation domain is larger than the source
- …
