A sampling strategy of the radiation operator in near-zone based on an asymptotic kernel

In 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

On the Singular Spectrum of the Radiation Operator for Multiple and Extended Observation Domains

The problem of studying how spatial diversity impacts on the spectrum (singular values) of the radiation operator is addressed. This topic is of great importance because of its connection with the so-called number of degrees of freedom concept which in turn is a key parameter in inverse source problems as well as to the problem of transmitting information by waves from a source domain to an observation domain. The case of a bounded rectilinear source with the radiated field observed over multiple bounded rectilinear domains parallel to the source is considered. Then, the analysis is generalized to two-dimensional extended observation domains. Analytical arguments are developed to estimate the pertinent singular value behavior. This allows highlighting the way observation domain features affect spectrum behavior. Numerical examples are shown to support the analytical results

Scattered Far-Field Sampling in Multi-Static Multi-Frequency Configuration

This paper deals with an inverse scattering problem under a linearized scattering model for a multi-static/multi-frequency configuration. The focus is on the determination of a sampling strategy that allows the reduction of the number of measurement points and frequencies and at the same time keeping the same achievable performance in the reconstructions as for full data acquisition. For the sake of simplicity, a 2D scalar geometry is addressed, and the scattered far-field data are collected. The relevant scattering operator exhibits a singular value spectrum that abruptly decays (i.e., a step-like behavior) beyond a certain index, which identifies the so-called number of degrees of freedom (NDF) of the problem. Accordingly, the sampling strategy is derived by looking for a discrete finite set of data points for which the arising semi-discrete scattering operator approximation can reproduce the most significant part of the singular spectrum, i.e., the singular values preceding the abrupt decay. To this end, the observation variables are suitably transformed so that Fourier-based arguments can be used. The arising sampling grid returns several data that is close to the NDF. Unfortunately, the resulting data points (in the angle-frequency domain) leading to a complicated measurement configuration which requires collecting the data at different spatial positions for each different frequency. To simplify the measurement configuration, a suboptimal sampling strategy is then proposed which, by an iterative procedure, enforces the sampling points to belong to a rectangular grid in the angle-frequency domain. As a result of this procedure, the overall data points (i.e., the couples angle-frequency) actually increase but the number of different angles and frequencies reduce and lead to a measurement configuration that is more practical to implement. A few numerical examples are included to check the proposed sampling scheme

Scattered Far-Field Sampling in Multi-Static Multi-Frequency Configuration

This paper deals with an inverse scattering problem under a linearized scattering model for a multi-static/multi-frequency configuration. The focus is on the determination of a sampling strategy that allows the reduction of the number of measurement points and frequencies and at the same time keeping the same achievable performance in the reconstructions as for full data acquisition. For the sake of simplicity, a 2D scalar geometry is addressed, and the scattered far-field data are collected. The relevant scattering operator exhibits a singular value spectrum that abruptly decays (i.e., a step-like behavior) beyond a certain index, which identifies the so-called number of degrees of freedom (NDF) of the problem. Accordingly, the sampling strategy is derived by looking for a discrete finite set of data points for which the arising semi-discrete scattering operator approximation can reproduce the most significant part of the singular spectrum, i.e., the singular values preceding the abrupt decay. To this end, the observation variables are suitably transformed so that Fourier-based arguments can be used. The arising sampling grid returns several data that is close to the NDF. Unfortunately, the resulting data points (in the angle-frequency domain) leading to a complicated measurement configuration which requires collecting the data at different spatial positions for each different frequency. To simplify the measurement configuration, a suboptimal sampling strategy is then proposed which, by an iterative procedure, enforces the sampling points to belong to a rectangular grid in the angle-frequency domain. As a result of this procedure, the overall data points (i.e., the couples angle-frequency) actually increase but the number of different angles and frequencies reduce and lead to a measurement configuration that is more practical to implement. A few numerical examples are included to check the proposed sampling scheme

The Role of Diversity on Linear Scattering Operator: The Case of Strip Scatterers Observed under the Fresnel Approximation

The aim of this paper is to investigate the role of multiple views and multiple frequencies in linear inverse scattering problems. The study was performed assuming the Fresnel-zone approximation on the scattering operator. Due to the crucial role played by singular values into analysing the linear inverse scattering problems, the impact of view and frequency diversities on singular values behaviour was established. In fact, the singular values were related to the most common metrics used to quantify the achievable performances in inverse scattering problems, such as the number of degrees of freedom (NDF), the information content and the resolution

Metric entropy in linear inverse scattering

The role of multiple views and/or multiple frequencies on the achievable performancein linear inverse scattering problems is addressed. In order to establish such a role, herethe impact of views and frequencies on the "information" that can be conveyed back from datato the unknown, is studied. For the sake of simplicity, the study deals with strip scatterers andthe cases of discrete angles of incidence and/or frequencies are tackled

Source's symmetries and priors: the effect on information content of radiated field

In this paper it is studied how certain symmetry priors affect some metrics commonly used to evaluate the achievable performance in linear inverse problems such as the Number of Degrees of Freedom (NDF), the point-spread function (psf) and Kolmogorov entropy

An Insight into the Warping Spatial Sampling Method in Subsurface Radar Imaging and Its Experimental Validation

In this paper, we are concerned with microwave subsurface imaging achieved by inverting the linearized scattering operator arising from the Born approximation. In particular, we consider the important question of reducing the required data to achieve imaging. This can help to reduce the radar system’s cost and complexity and mitigate the imaging algorithm’s computational burden and the needed storage resources. To cope with these issues, in the framework of a multi-monostatic/multi-frequency configuration, we introduce a new spatial sampling scheme, named the warping method, that allows for a significant reduction in spatial measurements compared to other literature approaches. The basic idea is to introduce some variable transformations that “warp” the measurement space so that the reconstruction point-spread function obtained by adjoint inversion is recast as a Fourier-like transformation, which provides insights into how to achieve the sampling. In our previous contributions, we focused on presenting and checking the theoretical background with simple numerical examples. In this contribution, we briefly review the key components of the warping method and present its experimental validation by considering a realistic subsurface scattering scenario for the case of a buried water pipe. Essentially, we show that the latter succeeds in reducing the number of data compared to other approaches in the literature, without significantly affecting the reconstruction results