Inverse Source Problem: A Comparison Between the Cases of Electric and Magnetic Sources

Abstract

Abstract-This work deals with the inverse source problem starting from the knowledge of the radiated field in the near field zone. The inverse problem is stated as the inversion of a linear integral equation and the Singular Value Decomposition (SVD) is exploited as an analysis and inversion tool. In particular, here, we deal with a 2D geometry and aim at comparing the features of the inverse problem in dependence on the nature of the source (electric or magnetic).

On the singular spectrum of radiation operators in the non-reactive zone: the case of strip sources

“…This is because the kernel function, being far from its singularity, behaves as an entire function of exponential type [10]. Numerical studies have been already presented in literature [17,18] confirming such a behavior. What is more a heuristic formula was provided in [17] relating the critical index mentioned above to the parameters of the radiation configuration.…”

“…A more interesting difference between the magnetic and the electric sources resides in the way they convey information. To be more precise, in [18] it has been numerically observed that while for the magnetic case the spatial spectral content carried out by the singular functions moves towards high frequencies as their index increases (within the relevant range ⋯ N 0, , ), for the electric source just the opposite is true. For readerʼs convenience, figure 4 shows the spectral content associated to different values of the SVD truncation index N T .…”

“…In order to address more general configurations the case of non-reactive zone has been numerically investigated in [17] for the magnetic currents and in [18] also for the electric case. With non-reactive zone it is meant that evanescent waves are negligible but no constraints on the source and the observation domains extents have been imposed as required by the far-zone or the Fresnel paraxial approximation.…”

Information Content in Inverse Source With Symmetry and Support Priors

“…This can be achieved by introducing a windowing sequences W n which multiplies the terms within the series in Eq. (2). The simplest approach is the truncated singular value decomposition (TSVD) [4] for which W n = 1 for 0 ≤ n ≤ N i and W n = 0 for n > N i , N i being the truncation index to be fixed according to "tolerable" noise level.…”

“…Actually, the problem setting requires defining not only the radiation operator G † but also the source and field functional spaces X and Y [1,2]. Both these spaces depend on the domains where s and f are supported.…”