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Variational Decomposition of Vector Fields in the Presence of Noise

P.D. Tafti, E. Bostan, M. Unser

Proceedings of the Tenth IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI'13), San Francisco CA, USA, April 7-11, 2013, pp. 1162-1165.

We present a variational framework, and an algorithm based on the alternating method of multipliers (ADMM), for the problem of decomposing a vector field into its curl- and divergence-free components (Helmholtz decomposition) in the presence of noise. We provide experimental confirmation of the effectiveness of our approach by separating vector fields consisting of a curl-free gradient field super-imposed on a divergence-free laminar flow corrupted by noise, as well as suppressing non-zero divergence distortions in a computational fluid dynamics simulation of blood flow in the thoracic aorta. The methods developed and presented here can be used in the analysis of flow-field images and in their correction and enhancement by enforcing suitable physical constraints such as zero divergence.

AUTHOR="Tafti, P.D. and Bostan, E. and Unser, M.",
TITLE="Variational Decomposition of Vector Fields in the Presence of
BOOKTITLE="Proceedings of the Tenth IEEE International Symposium on
        Biomedical Imaging: {F}rom Nano to Macro ({ISBI'13})",
address="San Francisco CA, USA",
month="April 7-11,",

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