Geometry-constrained Degrees of Freedom Analysis for Imaging Systems: Monostatic and Multistatic

TL;DR

This paper presents a theoretical framework for analyzing the degrees of freedom in electromagnetic imaging systems, revealing that geometry constrains information content and that monostatic and multistatic systems have equal DoF, with implications for resolution.

Contribution

It introduces the space-bandwidth product to accurately predict DoF and compares monostatic and multistatic architectures, extending prior Fresnel-based analyses.

Findings

SBP accurately predicts DoF under Born approximation

Monostatic and multistatic systems have equal DoF

Matched-filter reconstruction reduces resolution in multistatic systems

Abstract

In this paper, we develop a theoretical framework for analyzing the measurable information content of an unknown scene through an active electromagnetic imaging array. We consider monostatic and multistatic array architectures in a one-dimensional setting. Our main results include the following: (a) we introduce the space-bandwidth product (SBP), and show that, under the Born approximation, it provides an accurate prediction of the number of the degrees of freedom (DoF) as constrained by the geometry of the scene and the imaging system; (b) we show that both monostatic and multistatic architectures have the same number of DoF; (c) we show that prior DoF analysis based on the more restrictive Fresnel approximation are obtained by specializing our results; (d) we investigate matched-filter (back-propagation) and pseudoinverse image reconstruction schemes, and analyze the achievable resolution through these methods. Our analytical framework opens up new avenues to investigate image formation techniques that aim to reconstruct the reflectivity function of the scene by solving an inverse scattering problem, and provides insights on achievable resolution. For example, we show that matched-filter reconstruction leads to a significant resolution loss for multistatic architectures.