Variational decomposition of vector fields in the presence of noise
Biomedical Imaging（2013）
摘要
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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关键词
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,Helmholtz decomposition,alternating method of multipliers (ADMM),curl,divergence,flow-field imaging,variational methods,vector fields
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