Variational enhancement and denoising of flow field images

2012 9th IEEE International Symposium on Biomedical Imaging (ISBI)

Tafti

Unser

2012

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Recent advances in vector-field imaging have brought to the forefront the need for efficient denoising and reconstruction algorithms that take the physical properties of vector fields into account and can be applied to large volumes of data. With these requirements in mind, we propose a computationally efficient algorithm for variational denoising and reconstruction of vector fields. Our variational objective combines rotation-and scale-invariant regularization functionals that permit one to tune the algorithm to the physical characteristics of the underlying phenomenon. In addition, these regularization terms involve L1 norms in the spirit of total-variation (TV) regularization, which, as in the scalar case, leads to better preservation of discontinuities and superior SNR performance compared to its quadratic alternative. Some experimental results are provided to illustrate and verify the proposed scheme.

Section: Introductionmentioning

confidence: 99%

A dual algorithm for L<inf>1</inf>-regularized reconstruction of vector fields

2012 9th IEEE International Symposium on Biomedical Imaging (ISBI)

Tafti

Unser

2012

Self Cite

“…Continuing our previous line of work on vector field denoising and reconstruction in medical applications [2][3][4], in this paper we present a variational formulation and an algorithmic framework for Helmholtz decomposition of vector fields in the presence of noise. The essence of the formulation is to decompose the noisy vector field into three components: f cf (curl-free), f df (divergence-free), and n (noise), by minimising a suitable joint energy functional E( f cf , f df , n) subject to the constraint that these three components sum up to measurement vector y:…”

Section: Introductionmentioning

confidence: 93%

“…In practice, we work with discretised fields as well as discretised curl and divergence operators, which, in the simplest case, are based on finite differences [3,4]. Across field discontinuities (fluid interfaces, boundaries, etc.…”

Section: Problem Formulationmentioning

confidence: 99%

Variational decomposition of vector fields in the presence of noise

Tafti¹,

2013 IEEE 10th International Symposium on Biomedical Imaging

Unser

2013

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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.

“…For instance, Suter and Chen [4] and Arigovindan et al [5] have considered them in the context of quadratic (L2) regularization. Tafti and Unser [6] and Tafti et al [7] have showed that the discontinuities at the flow boundaries are better preserved by switching from an L2-norm to an L1-norm regularization.…”

Section: Introductionmentioning

confidence: 99%

“…They are not truly suited for dynamic-flow imaging applications. In the present paper, based on our previous approaches on flow-field reconstruction [6,7,8], we introduce a variational method for time-dependent volumetric flow-field data.…”

Section: Introductionmentioning

confidence: 99%

Spatio-temporal regularization of flow-fields

2013 IEEE 10th International Symposium on Biomedical Imaging

Vardoulis

Piccini

et al. 2013

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We introduce a novel variational framework for the regularized reconstruction of time-resolved volumetric flow fields. Our objective functional takes the physical characteristics of the underlying flow into account in both the spatial and the temporal domains. For an efficient minimization of the objective functional, we apply a proximal-splitting algorithm and perform parallel computations. To demonstrate the utility of our variational method, we first denoise a simulated flow-field in the human aorta and show that our method outperforms spatial-only regularization in terms of signal-to-noise ratio (SNR). We then apply the scheme to a real 3D+time phase-contrast MRI dataset and obtain high-quality visualizations.