Dynamic MRI Reconstruction via Weighted Tensor Nuclear Norm Regularizer

Cui, Kaiyan

doi:10.1109/jbhi.2021.3061793

Cited by 12 publications

(7 citation statements)

References 28 publications

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“…Considering the block-wise smoothness of tensor data, Liu et al [33] proposed a smooth TRPCA model. Subsequently, the weighted tensor nuclear norm was utilized to impose the low-rank nature in L [34]. However, the low-rank nature in [34] is based on the unfolding operation to define the tensor nuclear norm of three unfolding matrices, which still leads to the loss of spatio-temporal structural information to some extent.…”

Section: Introductionmentioning

confidence: 99%

“…Subsequently, the weighted tensor nuclear norm was utilized to impose the low-rank nature in L [34]. However, the low-rank nature in [34] is based on the unfolding operation to define the tensor nuclear norm of three unfolding matrices, which still leads to the loss of spatio-temporal structural information to some extent. Recently, tensor singular value decomposition (t-SVD) [35] has been proposed for the low-rank tensor recovery problem.…”

Section: Introductionmentioning

confidence: 99%

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Smooth Tensor Qatar Riyal Decomposition for Dynamic MRI Reconstruction

Xu¹,

Chen²,

Zeng³

et al. 2024

IEEE J. Biomed. Health Inform.

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Dynamic magnetic resonance imaging (dMRI) speed and imaging quality have always been a crucial issue in medical imaging research. Most existing methods characterize the tensor rank-based minimization to reconstruct dMRI from sampling k-t space data. However, (1) these approaches that unfold the tensor along each dimension destroy the inherent structure of dMR images. (2) they focus on preserving global information only, while ignoring the local details reconstruction such as the spatial piece-wise smoothness and sharp boundaries. To overcome these obstacles, we suggest a novel low-rank tensor decomposition approach by integrating tensor Qatar Riyal (QR) decomposition, low-rank tensor nuclear norm, and asymmetric total variation to reconstruct dMRI, named TQRTV. Specifically, while preserving the tensor inherent structure by utilizing tensor nuclear norm minimization to approximate tensor rank, QR decomposition reduces the dimensions in the lowrank constraint term, thereby improving the reconstruction performance. TQRTV further exploits the asymmetric total variation regularizer to capture local details. Numerical experiments demonstrate that the proposed reconstruction approach is superior to the existing ones.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Smooth Tensor Qatar Riyal Decomposition for Dynamic MRI Reconstruction

Xu¹,

Chen²,

Zeng³

et al. 2024

IEEE J. Biomed. Health Inform.

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show abstract

“…A joint Tucker rank and sparsity constrained model has also been developed to recover DMR images and use the tensor trace norm 25 as the convex relaxation of Tucker rank 26 . Some works 27,28 extend Tucker rank to (L+S) decomposition models. Although Tucker rank is successfully utilized in accelerating DMRI, each matrix

\mathbf {X}_{({n})}

is obtained by unfolding the tensor

\mathcal {X}

along a single mode.…”

Section: Introductionmentioning

confidence: 99%

Accelerated dynamic MR imaging with joint balanced low‐rank tensor and sparsity constraints

Liu

et al. 2023

Medical Physics

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BackgroundDynamic magnetic resonance imaging (DMRI) is an essential medical imaging technique, but the slow data acquisition process limits its further development.PurposeBy exploiting the inherent spatio‐temporal correlation of MR images, low‐rank tensor based methods have been developed to accelerate imaging. However, the tensor rank used by these methods is defined by an unbalanced matricization scheme, which cannot capture the global correlation of DMR data efficiently during the reconstruction process.MethodsIn this paper, an effective reconstruction model is proposed to achieve accurate reconstruction by using the tensor train (TT) rank defined by a well‐balanced matricization scheme to exploit the hidden correlation of DMR data and combining sparsity. Meanwhile, the ket augmentation (KA) technology is introduced to preprocess the DMR data into a higher‐order tensor through block structure addressing, which further improves the ability of TT rank to explore the local information of the image. In order to solve the proposed model, the alternating direction method of multipliers (ADMM) is used to decompose the optimization problem into several unconstrained subproblems.ResultsThe performance of the proposed method was validated on the 3D DMR image dataset by using different sampling trajectories and sampling rates. Extensive numerical experiments demonstrate that the reconstruction quality of the proposed method is superior to several state‐of‐the‐art reconstruction methods.ConclusionsThe proposed method successfully utilizes the TT rank to explore the global correlation of DMR images, enabling more detailed information of the image to be captured. Besides, with the sparse priors, the proposed method can further improve the overall reconstruction quality for highly undersampled MR images.

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“…Low-rank tensor priors have been introduced as powerful alternatives due to their improvement in recovered image quality [2,3,4]. Compared with matrix, tensor is a more natural representation for multi-frame dynamic MR data.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Cardiac MRI Reconstruction Using Combined Tensor Nuclear Norm and Casorati Matrix Nuclear Norm Regularizations

Zhang

2022

2022 IEEE 19th International Symposium on Biomedical Imaging (ISBI)

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Low-rank tensor models have been applied in accelerating dynamic magnetic resonance imaging (dMRI). Recently, a new tensor nuclear norm based on t-SVD has been proposed and applied to tensor completion. Inspired by the different properties of the tensor nuclear norm (TNN) and the Casorati matrix nuclear norm (MNN), we introduce a combined TNN and Casorati MNN regularizations framework to reconstruct dMRI, which we term as TMNN. The proposed method simultaneously exploits the spatial structure and the temporal correlation of the dynamic MR data. The optimization problem can be efficiently solved by the alternating direction method of multipliers (ADMM). In order to further improve the computational efficiency, we develop a fast algorithm under the Cartesian sampling scenario. Numerical experiments based on cardiac cine MRI and perfusion MRI data demonstrate the performance improvement over the traditional Casorati nuclear norm regularization method.

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Dynamic MRI Reconstruction via Weighted Tensor Nuclear Norm Regularizer

Cited by 12 publications

References 28 publications

Smooth Tensor Qatar Riyal Decomposition for Dynamic MRI Reconstruction

Smooth Tensor Qatar Riyal Decomposition for Dynamic MRI Reconstruction

Accelerated dynamic MR imaging with joint balanced low‐rank tensor and sparsity constraints

Dynamic Cardiac MRI Reconstruction Using Combined Tensor Nuclear Norm and Casorati Matrix Nuclear Norm Regularizations

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