Measuring Image Resolution in Ultrasound Localization Microscopy

Abstract

The resolution of an imaging system is usually determined by the width of its point spread function and is measured using the Rayleigh criterion. For most system, it is in the order of the imaging wavelength. However, super resolution techniques such as localization microscopy in optical and ultrasound imaging can resolve features an order of magnitude finer than the wavelength. The classical description of spatial resolution no longer applies and new methods need to be developed. In optical localization microscopy, the Fourier Ring Correlation has showed to be an effective and practical way to estimate spatial resolution for Single Molecule Localization Microscopy data. In this work, we wish to investigate how this tool can provide a direct and universal estimation of spatial resolution in Ultrasound Localization Microscopy. Moreover, we discuss the concept of spatial sampling in Ultrasound Localization Microscopy and demonstrate how the Nyquist criterion for sampling drives the spatial/temporal resolution tradeoff. We measured spatial resolution on five different datasets over rodent's brain, kidney and tumor finding values between 11~\mu \text{m} and 34~\mu \text{m} for precision of localization between 11~\mu \text{m} and 15~\mu \text{m}. Eventually, we discuss from those in vivo datasets how spatial resolution in Ultrasound Localization Microscopy depends on both the localization precision and the total number of detected microbubbles. This study aims to offer a practical and theoretical framework for image resolution in Ultrasound Localization Microscopy.