A Novel Analysis of Super-Resolution for Born-Iterative-Type Algorithms in Microwave Medical Sensing and Imaging

Abstract

Microwave medical sensing and imaging (MMSI) is a highly active research field. In MMSI, electromagnetic inverse scattering (EIS) is a commonly used technique that infers the internal characteristics of the diseased area by measuring the scattered field. It is worth noting that the image formed by EIS often exhibits the super-resolution phenomenon, which has attracted much research interest over the past decade. A classical perspective is that multiple scattering leads to super-resolution, but this is subject to debate. This paper aims to analyze the super-resolution behavior for Born-iterative-type algorithms for the following three aspects. Firstly, the resolution defined by the traditional Rayleigh criterion can only be applied to point scatterers. It does not suit general scatterers. By using the Sparrow criterion and the generalized spread function, the super-resolution condition can be derived for general scatterers even under the Born approximation (BA) condition. Secondly, an iterative algorithm results in larger coefficients in the high-frequency regime of the optical transfer function compared to non-iterative BA. Due to the anti-apodization effect, the spread function of the iterative method becomes steeper, which leads to a better resolution following the definition of the Sparrow criterion mentioned above. Thirdly, the solution from the previous iteration, as the prior knowledge for the next iteration, will cause changes in the total field, which provides additional information outside the Ewald sphere and thereby gives rise to super-resolution. Comprehensive numerical examples are used to verify these viewpoints.

Keywords

• super-resolution
• electromagnetic inverse scattering
• Sparrow criterion
• anti-apodization
• Born iterative methods