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

Bostan, Emrah; Lefkimmiatis, Stamatios; Vardoulis, Orestis; Stergiopulos, Nikolaos; Unser, Michaël

doi:10.1109/lsp.2014.2369212

Cited by 12 publications

(10 citation statements)

References 23 publications

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“…Numpy library was used for various matrix operations. For comparison, the proposed method was evaluated against the total variation method (TV) [1] and divergence-free wavelets with Sure-Shrink, median absolute deviation, and partial cycle spinning (DFW) [17] (where applicable). Both TV and DFW are the leading state-of-the-art denoising methods as shown in our previous study [8].…”

Section: Datamentioning

confidence: 99%

Time-resolved denoising using model order reduction, dynamic mode decomposition, and kalman filter and smoother

Fathi¹,

Baghaie²,

Bakhshinejad³

et al. 2020

Journal of Computational Dynamics

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In this research, we investigate the application of Dynamic Mode Decomposition combined with Kalman Filtering, Smoothing, and Wavelet Denoising (DMD-KF-W) for denoising time-resolved data. We also compare the performance of this technique with state-of-the-art denoising methods such as Total Variation Diminishing (TV) and Divergence-Free Wavelets (DFW), when applicable. Dynamic Mode Decomposition (DMD) is a data-driven method for finding the spatio-temporal structures in time series data. In this research, we use an autoregressive linear model resulting from applying DMD to the time-resolved data as a predictor in a Kalman Filtering-Smoothing framework for the purpose of denoising. The DMD-KF-W method is parameter-free and runs autonomously. Tests on numerical phantoms show lower error metrics when compared to TV and DFW, when applicable. In addition, DMD-KF-W runs an order of magnitude faster than DFW and TV. In the case of synthetic datasets, where the noise-free datasets were available, our method was shown to perform better than TV and DFW methods (when applicable) in terms of the defined error metric.

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Section: Datamentioning

confidence: 99%

Time-resolved denoising using model order reduction, dynamic mode decomposition, and kalman filter and smoother

Fathi¹,

Baghaie²,

Bakhshinejad³

et al. 2020

Journal of Computational Dynamics

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“…Multiple approaches exist to denoise PC‐MRI data [SNGP93, Buo94, FA03, LKTW12, BGWK13, BLV*15, OUT*15, KBvP*16, SKP18]. Some methods include the finite difference method [SNGP93], which projects the data onto a divergence‐free vector field.…”

Section: Related Workmentioning

confidence: 99%

“…They reduce its divergence, but might deviate from the measured data more than necessary, even if some methods actively try to minimize the difference between the outcome and the noisy input data, for example, Bostan et al . [BLV*15]. These techniques, on the contrary, mainly focus on making the data divergence free, and often do not consider the dependency on the modelled anatomy, are not compliant with Navier–Stokes equations nor allow for interpolation.…”

Section: Related Workmentioning

confidence: 99%

Data Assimilation for Full 4D PC‐MRI Measurements: Physics‐Based Denoising and Interpolation

Hoon

Jalba

Farag

et al. 2020

Computer Graphics Forum

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Phase‐Contrast Magnetic Resonance Imaging (PC‐MRI) surpasses all other imaging methods in quality and completeness for measuring time‐varying volumetric blood flows and has shown potential to improve both diagnosis and risk assessment of cardiovascular diseases. However, like any measurement of physical phenomena, the data are prone to noise, artefacts and has a limited resolution. Therefore, PC‐MRI data itself do not fulfil physics fluid laws making it difficult to distinguish important flow features. For data analysis, physically plausible and high‐resolution data are required. Computational fluid dynamics provides high‐resolution physically plausible flows. However, the flow is inherently coupled to the underlying anatomy and boundary conditions, which are difficult or sometimes even impossible to adequately model with current techniques. We present a novel methodology using data assimilation techniques for PC‐MRI noise and artefact removal, generating physically plausible flow close to the measured data. It also allows us to increase the spatial and temporal resolution. To avoid sensitivity to the anatomical model, we consider and update the full 3D velocity field. We demonstrate our approach using phantom data with various amounts of induced noise and show that we can improve the data while preserving important flow features, without the need of a highly detailed model of the anatomy.

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“…The regularization term ℛ(·) enforces physics of the flow such as divergence-free and/or curl-free conditions. Variants of Total variation (TV) regularization is used to solve the optimization problem(Tafti et al, 2011; Bostan et al, 2015a). The second set of techniques use projections on to various basis functions such as divergence-free wavelets(Ong et al, 2015; Deriaz and Perrier, 2006; Bostan et al, 2015b), divergence-free radial basis functions (Busch et al, 2013), and divergence-free vector fields using finite difference methods (Song et al, 1993).…”

Section: Introductionmentioning

confidence: 99%

Merging computational fluid dynamics and 4D Flow MRI using proper orthogonal decomposition and ridge regression

Bakhshinejad

Baghaie²,

Vali

et al. 2017

Journal of Biomechanics

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Time resolved phase-contrast magnetic resonance imaging 4D-PCMR (also called 4D Flow MRI) data while capable of non-invasively measuring blood velocities, can be affected by acquisition noise, flow artifacts, and resolution limits. In this paper, we present a novel method for merging 4D Flow MRI with computational fluid dynamics (CFD) to address these limitations and to reconstruct de-noised, divergence-free high-resolution flow-fields. Proper orthogonal decomposition (POD) is used to construct the orthonormal basis of the local sampling of the space of all possible solutions to the flow equations both at the low-resolution level of the 4D Flow MRI grid and the high-level resolution of the CFD mesh. Low-resolution, de-noised flow is obtained by projecting in-vivo 4D Flow MRI data onto the low-resolution basis vectors. Ridge regression is then used to reconstruct high-resolution de-noised divergence-free solution. The effects of 4D Flow MRI grid resolution, and noise levels on the resulting velocity fields are further investigated. A numerical phantom of the flow through a cerebral aneurysm was used to compare the results obtained using the POD method with those obtained with the state-of-the-art de-noising methods. At the 4D Flow MRI grid resolution, the POD method was shown to preserve the small flow structures better than the other methods, while eliminating noise. Furthermore, the method was shown to successfully reconstruct details at the CFD mesh resolution not discernible at the 4D Flow MRI grid resolution. This method will improve the accuracy of the clinically relevant flow-derived parameters, such as pressure gradients and wall shear stresses, computed from in-vivo 4D Flow MRI data.

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

Cited by 12 publications

References 23 publications

Time-resolved denoising using model order reduction, dynamic mode decomposition, and kalman filter and smoother

Time-resolved denoising using model order reduction, dynamic mode decomposition, and kalman filter and smoother

Data Assimilation for Full 4D PC‐MRI Measurements: Physics‐Based Denoising and Interpolation

Merging computational fluid dynamics and 4D Flow MRI using proper orthogonal decomposition and ridge regression

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