Super-resolution of 4D flow MRI through inverse problem explicit solving

Abstract: Four-dimensional Flow MRI (4D Flow MRI) enables non-invasive, time-resolved imaging of blood flow in three spatial dimensions, offering valuable insights into complex hemodynamics. However, its clinical utility is limited by low spatial resolution and poor signal-to-noise ratio (SNR), imposed by acquisition time constraints. In this work, we propose a novel method for super-resolution and denoising of 4D Flow MRI based on the explicit solution of an inverse problem formulated in the complex domain. Using clinically available magnitude and velocity images, we reconstruct complex-valued spatial signals and model resolution degradation as a convolution followed by subsampling. A fast, non-iterative algorithm is employed to solve the inverse problem independently for each velocity direction. We validate our method on synthetic data generated from computational fluid dynamics (CFD) and on physical phantom experiments acquired with 4D Flow MRI. Results demonstrate the potential of our approach to enhance velocity field resolution and reduce noise without the need for large training datasets or iterative solvers.