On the effects of spatial sampling quantization in super-resolution ultrasound microvessel imaging

Ultrasound super-resolution (SR) microvessel imaging technologies are rapidly emerging and evolving. The unprecedented combination of imaging resolution and penetration promises a wide range of preclinical and clinical applications. This paper concerns spatial quantization error in SR imaging, a common issue that involves a majority of current SR imaging methods. While quantization error can be alleviated by the microbubble localization process (e.g., via upsampling or parametric fitting), it is unclear to what extent the localization process can suppress the spatial quantization error induced by discrete sampling. It is also unclear when low spatial sampling frequency will result in irreversible quantization errors that cannot be suppressed by the localization process. This paper had two goals: 1) to systematically investigate the effect of quantization in SR imaging and establish principles of adequate SR imaging spatial sampling that yield minimal quantization error with proper localization methods and 2) to compare the performance of various localization methods and study the level of tolerance of each method to quantization. We conducted experiments on a small wire target and on a microbubble flow phantom. We found that the Fourier analysis of an oversampled spatial profile of the microbubble signal could provide reliable guidance for selecting beamforming spatial sampling frequency. Among various localization methods, parametric Gaussian fitting and centroid-based localization on upsampled data had better microbubble localization performance and were less susceptible to quantization error than peak intensity-based localization methods. When spatial sampling resolution was low, parametric Gaussian fitting-based localization had the best performance in suppressing quantization error, and could produce acceptable SR microvessel imaging with no significant quantization artifacts. The findings from this paper can be used in practice to help intelligently determine the minimum requirement of spatial sampling for robust microbubble localization to avoid adding or even reduce the burden of computational cost and data storage that are commonly associated with SR imaging.