Role of diversity on the singular values of linear scattering operators: the case of strip objects

Abstract

The singular value decomposition of the far-zone scattering operator for weak strip-like scattering objects is studied under multiple view and/or multiple frequency illuminations. The aim is to highlight how such diversities impact the number of degrees of freedom (NDF) of the scattering problem. When the angles of incidence and/or frequencies vary within discrete finite sets, the singular values are analytically determined. It is shown that they exhibit a multistep behavior. For the continuous case, upper and lower bounds are found, which allows us to obtain estimations for the NDF dependending on the parameters of the configuration.

Metric entropy in linear inverse scattering

“…In [12], it has been shown that in order to obtain the maximum number of measures 'linearly independent ' two extremal views (i.e., having angles corresponding to the edges of Ω o ) are sufficient. Accordingly, multiple views can be considered redundant.…”

“…A f is in a suitable form to apply the results reported in [12]. Hence, it has been shown that as long as c M = a∆k/2 1 and ak figure 6.…”

“…In [12], it has been concluded that while the maximum number of measurements 'linearly independent ' depends on the highest adopted frequency k max , by using more frequencies (lower than the highest one) shapes the singular . value behaviour so that it resemble a staircase.…”

“…In [12], the focus was addressed on how the diversities change both these attributes of the singular value behaviour. In particular, mathematical arguments that allow to analytically estimate the singular values were developed.…”

Information Content in Inverse Source With Symmetry and Support Priors

“…(12) [16]. By doing so, (see Appendix B for further details) the eigenspectrum of G r † G r can be approximated as ¶ (16) accounts for also the case uavg = 0.…”