Title :
Variational decomposition of vector fields in the presence of noise
Author :
Tafti, Pouya D. ; Bostan, Emrah ; Unser, Michael
Abstract :
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.
Keywords :
Gaussian noise; Helmholtz equations; biomedical MRI; blood; blood flow measurement; computational fluid dynamics; flow simulation; image denoising; image enhancement; medical image processing; variational techniques; Helmholtz decomposition; alternating method-of-multipliers; blood flow; computational fluid dynamics simulation; curl-free components; curl-free gradient field; divergence-free components; divergence-free laminar flow; flow-field image analysis; image correction; image enhancement; magnetic resonance imaging; noise; nonzero divergence distortions; thoracic aorta; variational decomposition; vector fields; Abstracts; Artificial intelligence; Noise; Visualization; Helmholtz decomposition; alternating method of multipliers (ADMM); curl; divergence; flow-field imaging; variational methods; vector fields;
Conference_Titel :
Biomedical Imaging (ISBI), 2013 IEEE 10th International Symposium on
Conference_Location :
San Francisco, CA
Print_ISBN :
978-1-4673-6456-0
DOI :
10.1109/ISBI.2013.6556689