Quantitative Analysis of Super Resolution in Electromagnetic Inverse Scattering for Microwave Medical Sensing and Imaging

Abstract

Microwave medical sensing and imaging (MMSI) has been a research hotspot in the past years. Imaging algorithms based on electromagnetic inverse scattering (EIS) play a key role in MMSI due to the super-resolution phenomenon. EIS problems generally employ far-field scattered data to reconstruct images. However, the far-field data do not include information outside the Ewald’s sphere, so theoretically it is impossible to achieve super resolution. The reason for super resolution has not been clarified. The majority of the current research focuses on how nonlinearity affects the super-resolution phenomena in EIS. However, the mechanism of super-resolution in the absence of nonlinearity is routinely ignored. In this research, we address a prevalent yet overlooked problem where the image resolution due to scatterers of extended structures is incorrectly analyzed using the model of point scatterers. Specifically, the classical resolution of EIS is defined by the Rayleigh criterion which is only suitable for point-like scatterers. However, the super-resolution in EIS is often observed for general scatterers like cylinders, squares or Austria shapes. Subsequently, we provide theoretical results for the Born approximation framework in EIS, and employ the Sparrow criteria to quantify the resolution for symmetric objects of extended structures. Furthermore, the modified Sparrow criterion is proposed to calculate the resolution of asymmetric scatterers. Numerical examples show that the proposed approach can better explain the super-resolution phenomenon in EIS.

Keywords

• electromagnetic inverse problems
• resolution
• super-resolution
• point spread function
• Rayleigh criterion
• Sparrow criterion