Influence of Image Discretization and Patch Size on ULM Localization Precision

To obtain super-resolved maps of the microvasculature using ultrasound localization microscopy, the localization precision of the microbubbles (MB) is essential. However, previous studies showed some counterintuitive results across different localization methods and image discretizations. Therefore, this study systematically analyzes the influence of image discretization and patch size on localization precision to derive guidelines for a good choice of parameters. For this purpose, we simulated MB images with Gaussian point-spread functions (PSF) of varying width σ at randomly generated subpixel positions. Rician distributed noise was added. The MB localizations were carried out on patches of different sizes (number of pixels N × N). We investigated two localization techniques: a parametric Gaussian fit and the radial symmetry method. For the Gaussian fit, the localization error is Gaussian distributed around zero and achieved standard deviations (STD) of about 0.03 times the pixel size Δ at its optimum performance. However, as the ratio of PSF width σ to pixel size Δ decreases to σ⁄Δ ≈ 0. 4, the error distribution becomes bimodal across all patch sizes, resulting in an increased localization STD of around 0.1Δ. With even smaller ratios, the STD deteriorates completely. For too small patches, the STD also increases, because only the peak region of the PSF is used for localization. The same findings apply to the radial symmetry method, albeit with slightly lower precision. Based on our results, we conclude that for precise MB localization, the necessary pixel (voxel) size Δ in each direction (axial, lateral, and elevational in case of 3D) is determined only indirectly by the wavelength but mainly by the width σ of the PSF. The ratio of PSF width to pixel size should be σ⁄Δ ≥ 0.6. Regarding the patch size, the rule N ≥ 2σ⁄Δ + 3 is recommended.