A novel approach using Cholesky decomposition-based neural networks for the estimation of Reynolds stress tensors in 4D Flow MRI is presented. Evaluation is carried out for simulated MRI signals using particle tracking velocimetry data and tested on in-vivo data obtained in a healthy volunteer and a patient with bioprosthetic aortic valve. The proposed method allows to account for non-Gaussian acquisition noise and guarantees positive-definiteness of the estimated tensors, which yields 68% improvement in turbulent shear stress estimation compared to standard least squares estimation.
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