BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

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. 

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AUTHOR="Tafti, P.D. and Bostan, E. and Unser, M.",
TITLE="Variational Decomposition of Vector Fields in the Presence of
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