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

On the Sampling of the Fresnel Field Intensity over a Full Angular Sector

In this article, the question of how to sample the square amplitude of the radiated field in the framework of phaseless antenna diagnostics is addressed. In particular, the goal of the article is to find a discretization scheme that exploits a non-redundant number of samples and returns a discrete model whose mathematical properties are similar to those of the continuous one. To this end, at first, the lifting technique is used to obtain a linear representation of the square amplitude of the radiated field. Later, a discretization scheme based on the Shannon sampling theorem is exploited to discretize the continuous model. More in detail, the kernel of the related eigenvalue problem is first recast as the Fourier transform of a window function, and after, it is evaluated. Finally, the sampling theory approach is applied to obtain a discrete model whose singular values approximate all the relevant singular values of the continuous linear model. The study refers to a strip source whose square magnitude of the radiated field is observed in the Fresnel zone over a 2D observation domain

Sampling Design of Synthetic Volume Arrays for Three-Dimensional Microwave Imaging

In this paper, sampling design of three-dimensional (3-D) synthetic array (i.e., synthetic volume array) for microwave imaging is considered. Generally, the spatial sampling criteria for one- or two-dimensional arrays can be determined based on some narrowband/ultrawideband array theories. However, for 3-D arrays, where antennas are located in a volume instead of over a surface, these existing array theories are no longer straightforwardly applicable. To address the spatial sampling problem of 3-D arrays, we formulate it as a sensor/observation selection problem in this paper. Although some selection approaches exist and are conveniently applicable to small-scale problems, they are either less efficient or provide less optimal results for selection problems with data dimensions of hundreds or even thousands which is typical for microwave imaging. To get the (near-) optimal spatial sampling scheme for 3-D arrays, a greedy algorithm named clustered maximal projection on minimal eigenspace (CMPME) is proposed to select the most informative sampling positions based on some optimality criteria. This algorithm attempts to select the fewest sampling positions by considering an error threshold for the estimated images. Moreover, it has higher computational efficiency compared to the existing approaches. Finally, its effectiveness and selection performances are demonstrated through some imaging examples.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Microwave Sensing, Signals & System