A dual algorithm for L&lt;inf&gt;1&lt;/inf&gt;-regularized reconstruction of vector fields

Bostan, Emrah; Tafti, Pouya D.; Unser, Michaël

doi:10.1109/isbi.2012.6235876

Cited by 6 publications

(8 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Figure 3 shows streamline visualisations of the same two fields, produced using EnSight (CEI, NC, USA). In addition to suppressing the non-zero-divergence distortion in the flow, in terms of noise reduction, for the sum of the two terms we achieved an SNR improvement from 10 dB to 10.97 dB, which is comparable with the state of the art [2,3]. Note that all these results were obtained without any substantial optimisation of algorithm parameters.…”

Section: Methodssupporting

confidence: 56%

“…The curl-free field in question was the gradient of the function φ(x, y, z) 2] with sampling step 0.1. For the incompressible component we simulated a laminar flow with a typical parabolic intensity profile inside a cylindrical pipe of radius 1 oriented along the z axis.…”

Section: Methodsmentioning

confidence: 99%

“…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%

See 2 more Smart Citations

Variational decomposition of vector fields in the presence of noise

Tafti¹,

Bostan

Unser

2013

2013 IEEE 10th International Symposium on Biomedical Imaging

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Methodssupporting

confidence: 56%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 93%

See 1 more Smart Citation

Variational decomposition of vector fields in the presence of noise

Tafti¹,

Bostan

Unser

2013

2013 IEEE 10th International Symposium on Biomedical Imaging

Self Cite

View full text Add to dashboard Cite

show abstract

“…For all methods, we use the same optimization algorithm that combines the duality arguments with Nesterov's method [18]. Note that this algorithm has been developed in [19] for , and in [10], [20], [21] for the existing vectorial extensions of TV. In all cases, the stopping criterion is set to either reaching a relative -normed difference of between two successive estimates, or a maximum of 500 iterations.…”

Section: Resultsmentioning

confidence: 99%

Improved Variational Denoising of Flow Fields with Application to Phase-Contrast MRI Data

Bostan

Lefkimmiatis

Vardoulis

et al. 2015

IEEE Signal Process. Lett.

Self Cite

View full text Add to dashboard Cite

We propose a new variational framework for the problem of reconstructing flow fields from noisy measurements. The formalism is based on regularizers penalizing the singular values of the Jacobian of the field. Specifically, we rely on the nuclear norm. Our method is invariant with respect to fundamental transformations and can be efficiently solved. We conduct numerical experiments on several phantom data and report improved performance compared to existing vectorial extensions of total variation and curl-divergence regularizations. Finally, we apply our reconstruction method to an experimentally-acquired phase-contrast MRI recording for enhancing the data visualization.

show abstract

“…Inspired by [28], a generalized regularization term is proposed in [14], we can convert the (3) into (4):…”

Section: B Our Framework For Non-blind Image Deblurringmentioning

confidence: 99%

Non-Blind Image Deblurring Method by the Total Variation Deep Network

et al. 2019

View full text Add to dashboard Cite

There are a lot of non-blind image deblurring methods, especially with the total variation (TV) model-based method. However, how to choose the parameters adaptively for regularization is a major open problem. We proposed a very novel method that is based on the TV deep network to learn the best parameters adaptively for regularization. We used deep learning and prior knowledge to set up a TV-based deep network and calculate the parameters of regularization, such as biases and weights. Therefore, we used the idea of a deep network to update these parameters automatically to avoid sophisticated calculations. Our experimental results by our proposed network are significantly better than several other methods, in respect of detail retention and anti-noise performance. At the same time, we can achieve the same effect with a minimum number of training sets, thus speeding up the calculation. INDEX TERMS Non-blind image deblurring, total variation model, deep learning.

show abstract

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

Cited by 6 publications

References 10 publications

Variational decomposition of vector fields in the presence of noise

Variational decomposition of vector fields in the presence of noise

Improved Variational Denoising of Flow Fields with Application to Phase-Contrast MRI Data

Non-Blind Image Deblurring Method by the Total Variation Deep Network

Contact Info

Product

Resources

About