Characterization of Direct Localization Algorithms for Ultrasound Super-Resolution Imaging in a Multibubble Environment: A Numerical and Experimental Study

Localization plays a significant role in the production of ultrasound localization microscopy images. For instance, detecting more microbubbles reduces the time of acquisition, while localizing them more accurately improves the resolution of the images. Previous approaches to compare the multiple localization algorithms rely on numerical simulation of a single steady microbubble, with or without modeling its nonlinear response. In real-life situations, vessels have a nonconstant velocity profile, which creates relative movement, producing dynamically overlapped microbubbles even at low concentrations. These complexities deteriorate the behavior of the localization algorithms. To incorporate these effects on the characterization of the localization methods, we designed a virtual medium containing four microtubes of different inner diameters, where single-pixel microbubbles were allowed to flow within each microtube with a parabolic velocity profile. A finite difference method was used to simulate the propagation of ultrasound waves to obtain B-mode images that fed four direct microbubbles localization algorithms (i.e., weighted centroid, 2D-spline interpolation, parabolic fitting, and onset detection). The performance of these methods was quantified using the number of microbubbles detected, the microbubbles distribution, the full width at half maximum, the maximum velocity, and the computational time as metrics. Our simulation results suggest that 2D-spline and paraboloid fitting were the best methods, detecting 100% of the microbubbles with an error in their distribution of 249 and 244 microbubbles, respectively. Both methods with a computational time cost of 18% and 7% lower than weighted centroid, respectively. We also present an experimental comparison of these localization methods, finding results similar to the numerical ones.