EPFL | Biomedical Imaging Group | Variational Denoising

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

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

2015 Twenty-Second IEEE International Conference on Image Processing (ICIP'15), Québec QC, Canada, September 27-30, 2015, paper no. TEC-P19.5.

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.

This abstract was originally published as E. Bostan, S. Lefkimmiatis, O. Vardoulis, N. Stergiopulos, M. Unser, "Improved Variational Denoising of Flow Fields with Application to Phase-Contrast MRI Data," IEEE Signal Processing Letters, vol. 22, no. 6, pp. 762-766, June 2015.

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