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

Resolution analysis of a volumetric coded aperture X-ray diffraction imaging system

BACKGROUND

A coded aperture X-ray diffraction (XRD) imaging system can measure the X-ray diffraction form factor from an object in three dimensions -X, Y and Z (depth), broadening the potential application of this technology. However, to optimize XRD systems for specific applications, it is critical to understand how to predict and quantify system performance for each use case.

OBJECTIVE

The purpose of this work is to present and validate 3D spatial resolution models for XRD imaging systems with a detector-side coded aperture.

METHODS

A fan beam coded aperture XRD system was used to scan 3D printed resolution phantoms placed at various locations throughout the system's field of view. The multiplexed scatter data were reconstructed using a model-based iterative reconstruction algorithm, and the resulting volumetric images were evaluated using multiple resolution criteria to compare against the known phantom resolution. We considered the full width at half max and Sparrow criterion as measures of the resolution and compared our results against analytical resolution models from the literature as well as a new theory for predicting the system resolution based on geometric arguments.

RESULTS

We show that our experimental measurements are bounded by the multitude of theoretical resolution predictions, which accurately predict the observed trends and order of magnitude of the spatial and form factor resolutions. However, we find that the expected and observed resolution can vary by approximately a factor of two depending on the choice of metric and model considered. We observe depth resolutions of 7-16 mm and transverse resolutions of 0.6-2 mm for objects throughout the field of view. Furthermore, we observe tradeoffs between the spatial resolution and XRD form factor resolution as a function of sample location.

CONCLUSION

The theories evaluated in this study provide a useful framework for estimating the 3D spatial resolution of a detector side coded aperture XRD imaging system. The assumptions and simplifications required by these theories can impact the overall accuracy of describing a particular system, but they also can add to the generalizability of their predictions. Furthermore, understanding the implications of the assumptions behind each theory can help predict performance, as shown by our data's placement between the conservative and idealized theories, and better guide future systems for optimized designs.

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

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.