Model-based deep learning for ultrasound localization microscopy

Ultrasound localization microscopy (ULM) effectively visualizes vasculature through localization of microbubbles using ultrasound. However, challenges arise from the domain gap between clean data from controlled lab environments and real-world scenarios. Factors, such as high bubble densities, reduced frame rates, and poor image quality (e.g., due to aberration), impede clinical adoption. Traditional methods face limitations in handling the challenging nature of ULM, which have spurred the integration of data-driven techniques. We specifically focus on model-based deep learning, emphasizing statistical inference techniques for increased robustness on out-of-distribution data. The localization task is expressed as an inverse problem y = Hx + n, where y, x, and n represent the observed ultrasound signal, underlying microbubble localizations, and noise. Inaccuracies in the measurement matrix H arise from oversimplified ultrasound acquisition models (i.e., aberration distorting the point-spread function), necessitating the application of spatial priors to regularize the forward model. The ISTA algorithm can enforce sparsity on x and help solve the ill-posed inverse problem. A deep learning extension, namely learned ISTA, can additionally mitigate errors in the forward model. Beyond spatial priors, imposing temporal priors on individual microbubbles enhances accuracy. KalmanNet, integrating Kalman filtering with deep learning, exemplifies this approach by effectively learning the temporal dynamics of microbubbles.