A fast 4D B-spline framework for model-based reconstruction and regularization in vector flow imaging

A generic framework for model-based regularization and reconstruction is described, with applications in a wide range of noisy measurement scenarios. The framework employs automatic differentiation and stochastic gradient optimizers to perform online measurement fitting and regularization, and was implemented as a scalable CPU and GPU library with highperformance operation even in compute- or memory-intensive contexts, such as for 4D cardiac vector flow imaging. The framework was demonstrated by reconstructing 4D vector flow mapping through the incorporation of the incompressible NavierStokes equations. Furthermore, the achieved performance was within bedside applicability requirements.