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. 

@INPROCEEDINGS(http://bigwww.epfl.ch/publications/tafti1301.html,
AUTHOR="Tafti, P.D. and Bostan, E. and Unser, M.",
TITLE="Variational Decomposition of Vector Fields in the Presence of
	Noise",
BOOKTITLE="Proceedings of the Tenth IEEE International Symposium on
	Biomedical Imaging: {F}rom Nano to Macro ({ISBI'13})",
YEAR="2013",
editor="",
volume="",
series="",
pages="1162--1165",
address="San Francisco CA, USA",
month="April 7-11,",
organization="",
publisher="",
note="")

© 2013 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.