Influence of Image Discretization and Patch Size on Microbubble Localization Precision

For ultrasound localization microscopy, the localization of microbubbles (MBs) is an essential part to obtain super-resolved maps of the vasculature. This article analyzes the impact of image discretization and patch size on the precision of different MB localization methods to reconcile different observations from previous studies, provide an estimate of feasible localization precision, and derive guidelines for an optimal parameter selection. For this purpose, the images of MBs were simulated with Gaussian point-spread functions (PSFs) of varying width parameter $\boldsymbol {\sigma }$ at randomly generated subpixel positions, and Rician distributed noise was added. Four localization methods were tested on the patches of different sizes (number of pixels ${N}\times {N}$ ): Gaussian fit (GF), radial symmetry (RS) method, calculation of center of mass (CoM), and peak detection (PD). Additionally, the Cramér-Rao lower bound (CRLB) for the given estimation problem was calculated. Our results show that the localization precision is strongly influenced by the ratio of the PSF width parameter $\boldsymbol {\sigma }$ to the pixel size $\boldsymbol {\Delta }$ , as well as the patch size N. The best parameter combination depends on the localization method. Generally, very small $\boldsymbol {\sigma /}{\boldsymbol {\Delta }}$ ratios as well as large $\boldsymbol {\sigma /}{\boldsymbol {\Delta }}$ ratios in combination with small N lead to performance degradation. The GF as a representative of a model-based fit comes close to the CRLB and always performs best for the $\boldsymbol {\sigma /}{\boldsymbol {\Delta }}$ ratios given by image discretization if N is adapted to the PSF. To achieve good results with the GF and the RS method, a good rule of thumb is to set the pixel sizes ${\boldsymbol {\Delta }}\boldsymbol {\le \sigma /0.6}$ and the patch sizes ${{N}\ge {2}\sigma /}\boldsymbol {\Delta }{+3}$ .