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

Zhang, Yinghao; Hu, Yue

doi:10.1109/isbi52829.2022.9761409

Cited by 8 publications

(6 citation statements)

References 8 publications

(7 reference statements)

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“…After all other variables are updated in each iteration,  n+1 is obtained by using the conjugate gradient method to solve the least squares problem (20).…”

Section: Solving Algorithmmentioning

confidence: 99%

“…As the natural representation of higher-order data, the tensor can preserve the structural information of the DMR images. 19,20 Similar to matrices, the low-rank property of tensors can also be used to recover missing elements in high-dimensional data, but the rank of tensors is not uniquely defined. The classical tensor ranks include the canonical polyadic (CP) rank and the Tucker rank.…”

Section: Introductionmentioning

confidence: 99%

“…A powerful mathematical tool, the tensor, has received great attention recently to solve this problem. As the natural representation of higher‐order data, the tensor can preserve the structural information of the DMR images 19,20 . Similar to matrices, the low‐rank property of tensors can also be used to recover missing elements in high‐dimensional data, but the rank of tensors is not uniquely defined.…”

Section: Introductionmentioning

confidence: 99%

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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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“…After all other variables are updated in each iteration,  n+1 is obtained by using the conjugate gradient method to solve the least squares problem (20).…”

Section: Solving Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Liu

et al. 2023

Medical Physics

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“…Ai et al introduced the t-SVD to dynamic MRI reconstruction by combining the convex relaxation of t-SVD, the TNN, and the l 1 norm of tensor gradient [39]. Zhang et al proposed to combine the TNN and Casorati matrix nuclear norm regularizers to reconstruct dMRI [40]. It is worth noting that with the vigorous development of artificial intelligence, more and more researchers have applied deep learning theory to various fields and made remarkable achievements [41]- [44].…”

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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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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“…model(Zhang et al 2022) is a variant of the L + S model(Otazo et al 2015), which decomposes the data into a low-rank component and a sparse component. In this model, Fourier transform along the time dimension F t is applied to the S component to enhance its sparsity, and quadratic term is used to relax the constraints.…”

mentioning

confidence: 99%

Accelerated partial separable model using dimension-reduced optimization technique for ultra-fast cardiac MRI

Sun

Liu

et al. 2023

Phys. Med. Biol.

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Objective. Imaging dynamic object with high temporal resolution is challenging in magnetic resonance imaging (MRI). Partial separable (PS) model was proposed to improve the imaging quality by reducing the degrees of freedom of the inverse problem. However, PS model still suffers from long acquisition time and even longer reconstruction time. The main objective of this study is to accelerate the PS model, shorten the time required for acquisition and reconstruction, and maintain good image quality simultaneously. Approach. We proposed to fully exploit the dimension-reduction property of the PS model, which means implementing the optimization algorithm in subspace. We optimized the data consistency term, and used a Tikhonov regularization term based on the Frobenius norm of temporal difference. The proposed dimension-reduced optimization technique was validated in free-running cardiac MRI. We have performed both retrospective experiments on public dataset and prospective experiments on in-vivo data. The proposed method was compared with four competing algorithms based on PS model, and two non-PS model methods. Main results. The proposed method has robust performance against shortened acquisition time or suboptimal hyper-parameter settings, and achieves superior image quality over all other competing algorithms. The proposed method is 20-fold faster than the widely accepted PS+Sparse method, enabling image reconstruction to be finished in just a few seconds. Significance. Accelerated PS model has the potential to save much time for clinical dynamic MRI examination, and is promising for real-time MRI applications.

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

Cited by 8 publications

References 8 publications

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

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

Smooth Tensor Qatar Riyal Decomposition for Dynamic MRI Reconstruction

Accelerated partial separable model using dimension-reduced optimization technique for ultra-fast cardiac MRI

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