MRI TV-Rician Denoising

Martín, Adrián; Garamendi, J. F.; Schiavi, Emanuele

doi:10.1007/978-3-642-38256-7_17

Cited by 8 publications

(19 citation statements)

References 13 publications

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“…We also test the numerical convergence of the p-approximating problems. Then, we compare TV-Rician with previously proposed methods for TV Rician-based denoising (Martin et al, 2011;Getreuer et al, 2011a;Chen and Zeng, 2015) for different images and noise intensities. Finally we present an application on real Diffusion Tensor Images (DTI), which is an MRI modality heavily affected by Rician noise (Basu et al, 2006;Tristán-Vega and Aja-Fernández, 2010).…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In order to cope with the difficulties of the non-smooth nonconvex problem (8), several methods have been proposed for TV-based denoising of Rician contaminated images. The first of them uses an ε-approximation of the TV term (Martin et al, 2011;Getreuer et al, 2011a) to obtain a smooth minimization problem. With this regularization, a gradient descent can be applied to solve the problem.…”

Section: Comparison With Other Variational Methods For Rician Denoisingmentioning

confidence: 99%

“…In fact, this non-convexity of the energy functional is crucial because otherwise we could show uniqueness of the trivial solution u ≡ 0. The variational minimization problem associated to the model equation we consider was proposed in (Martin et al, 2011), where the multivalued Euler-Lagrange equation for the 1-Laplacian operator is deduced as a first order necessary optimality condition. This minimization problem was simultaneously and independently considered in (Getreuer et al, 2011a), where blurring effects were included and existence and comparison results in the pure denoising case were reported.…”

Section: Introductionmentioning

confidence: 99%

“…This minimization problem was simultaneously and independently considered in (Getreuer et al, 2011a), where blurring effects were included and existence and comparison results in the pure denoising case were reported. In order to cope with the multivalued Euler-Lagrange equation an ε-regularization of the TV term was introduced in both works (Martin et al, 2011;Getreuer et al, 2011a) . More recently, in (Chen and Zeng, 2015) a convex variational model for restoring blurred images corrupted by Rician noise have been proposed to overcome the difficulties related to the non-convex nature of the original problem we are considering here.…”

Section: Introductionmentioning

confidence: 99%

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On 1-Laplacian Elliptic Equations Modeling Magnetic Resonance Image Rician Denoising

2016

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Modeling magnitude Magnetic Resonance Images (MRI) Rician denoising in a Bayesian or generalized Tikhonov framework using Total Variation (TV) leads naturally to the consideration of nonlinear elliptic equations. These involve the so called 1-Laplacian operator and special care is needed to properly formulate the problem. The Rician statistics of the data are introduced through a singular equation with a reaction term defined in terms of modified first order Bessel functions. An existence theory is provided here together with other qualitative properties of the solutions. Remarkably, each positive global minimum of the associated functional is one of such solutions. Moreover, we directly solve this non-smooth non-convex minimization problem using a convergent Proximal Point Algorithm. Numerical results based on synthetic and real MRI demonstrate a better performance of the proposed method when compared to previous TV based models for Rician denoising which regularize or convexify the problem. Finally, an application on real Diffusion Tensor Images, a strongly affected by Rician noise MRI modality, is presented and discussed.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Comparison With Other Variational Methods For Rician Denoisingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On 1-Laplacian Elliptic Equations Modeling Magnetic Resonance Image Rician Denoising

2016

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“…21 However, these noise models are different from the Rician distribution present in degraded MR images. To cope with such a problem, TV-based MRI Rician denoising models 13,22 have been proposed in the maximum a posteriori (MAP) framework. However, the reconstructed images often suffer from undesirable artifacts and block-like structures.…”

Section: A Background and Related Workmentioning

confidence: 99%

A two‐step optimization approach for nonlocal total variation‐based Rician noise reduction in magnetic resonance images

Liu

Shi

et al. 2015

Medical Physics

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This study describes and validates a nonlocal feature-preserving method for Rician noise reduction on synthetic and real MRI data sets. By exploiting the feature-preserving capability of NLTV regularizer, the proposed method maintains a good balance between noise reduction and fine detail preservation. The experiments have demonstrated a huge potential of the proposed method for routine clinical practice.

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