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Improved Variational Denoising of Flow Fields with Application to Phase-Contrast MRI Data

E. Bostan, S. Lefkimmiatis, O. Vardoulis, N. Stergiopulos, M. Unser

IEEE Signal Processing Letters, vol. 22, no. 6, pp. 762-766, June 2015.

We propose a new variational framework for the problem of reconstructing flow fields from noisy measurements. The formalism is based on regularizers penalizing the singular values of the Jacobian of the field. Specifically, we rely on the nuclear norm. Our method is invariant with respect to fundamental transformations and can be efficiently solved. We conduct numerical experiments on several phantom data and report improved performance compared to existing vectorial extensions of total variation and curl-divergence regularizations. Finally, we apply our reconstruction method to an experimentally-acquired phase-contrast MRI recording for enhancing the data visualization.

Supplementary material

  • Supplementary Note (PDF file) (139 Kb). Proof that the TVp regularizers are invariant under translation, scaling (up to a multiplicative factor), and rotation.

AUTHOR="Bostan, E. and Lefkimmiatis, S. and Vardoulis, O. and
        Stergiopulos, N. and Unser, M.",
TITLE="Improved Variational Denoising of Flow Fields with Application to
        Phase-Contrast {MRI} Data",
JOURNAL="{IEEE} Signal Processing Letters",

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