Accelerated dynamic MRI exploiting sparsity and low-rank structure: k-t SLR

By Sajan Goud Lingala, Yue Hu, E. D. Bella, Mathews Jacob. IEEE Transactions on Medical Imaging, 2011

702 citations recorded by the source corpus.

We introduce a novel algorithm to reconstruct dynamic magnetic resonance imaging (MRI) data from under-sampled k-t space data. In contrast to classical model based cine MRI schemes that rely on the sparsity or banded structure in Fourier space, we use the compact representation of the data in the Karhunen Louve transform (KLT) domain to exploit the correlations in the dataset. The use of the data-dependent KL transform makes our approach ideally suited to a range of dynamic imaging problems, even when the motion is not periodic. In comparison to current KLT-based methods that rely on a two-step approach to first estimate the basis functions and then use it for reconstruction, we pose the problem as a spectrally regularized matrix recovery problem. By simultaneously determining the temporal basis functions and its spatial weights from the entire measured data, the proposed scheme is capable of providing high quality reconstructions at a range of accelerations. In addition to using the compact representation in the KLT domain, we also exploit the sparsity of the data to further improve the recovery rate. Validations using numerical phantoms and in vivo cardiac perfusion MRI data demonstrate the significant improvement in performance offered by the proposed scheme over existing methods.

Subfields: Computational Mechanics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/7a22c2061d7161a2966b6a50abdb01a97c785ea0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

Low-Rank Modeling of Local k-Space Neighborhoods (LORAKS) for Constrained MRI (2014, background): “-norm (with ) problem formulations are observed to outperform nuclear norm formulations in a wide range of applications [2], [27], [32], [48], [54], [57].”
Magnetic resonance image reconstruction from undersampled measurements using a patch-based nonlocal operator (2014, methodology): “, 2010) and combined with low-rank strcture (Lingala et al., 2011; Zhao et al., 2012).”
A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction (2017, methodology): “For 2D reconstruction, the proposed method is compared to Dictionary Learning MRI (DLMRI) [2] and for dynamic reconstruction, the method is compared to Dictionary Learning with Temporal Gradient (DLTG) [3], kt Sparse and Low-Rank (kt-SLR) [20] and Low-Rank Plus Sparse Matrix Decomposition (L+S) [21]”
MoDL: Model-Based Deep Learning Architecture for Inverse Problems (2017, background): “Carefully engineered priors including total variation [5], patch-based non-local methods, low-rank penalties [6], [7], as well as priors learned from exemplary data [8] or the measurements themselves [9] are widely used.”
Low-rank and Sparse Matrix Decomposition for Accelerated Dynamic MRI with Separation of Background and Dynamic Components (2014, methodology): “The ideas introduced in the k-t SLR technique (14) and joint partial separability and sparsity method (15) also represent a combination of compressed sensing and low-rank matrix completion.”
Convolutional Recurrent Neural Networks for Dynamic MR Image Reconstruction (2017, neutral): “We compared the proposed method with the representative algorithms of the CS-based dynamic MRI reconstruction, such as k-t FOCUSS [1] and k-t SLR [2], and two variants of 3D CNN networks named 3D CNN-S and 3D CNN in our experiments.”
Deep Convolutional Neural Network for Inverse Problems in Imaging (2016, background): “el.unser@epﬂ.ch). November 14, 2016 DRAFT arXiv:1611.03679v1 [cs.CV] 11 Nov 2016 2 have been particularly inﬂuential in the ﬁeld of biomedical imaging, e.g., in magnetic resonance imaging (MRI) [10], [11] and X-ray computed tomography (CT) [12], [13]. These devices face an unfavorable trade-off betw”
A Deep Cascade of Convolutional Neural Networks for MR Image Reconstruction (2017, methodology): “lization of their reconstructions can be found in the following section. 2) Comparison with State-of-the-art: In this experiment, we compared our model with state-of-the-art methods: DLTG [3], kt-SLR [20] and L+S [21] for reconstructing the dynamic sequence. We compared the results for 3, 6, 9 and 1”
Accelerating magnetic resonance imaging via deep learning (2016, background): “Sparsity is one commonly used prior information due to the emergence of Compressed sensing (CS) and there are also other priors being considered, such as low-rank [7], statistics distribution regularization [8], manifold fitting [9], generalized series (GS) model [10] and so on.”
Deep Generative Adversarial Neural Networks for Compressive Sensing (GANCS) MRI (2018, background): “To render the MRI reconstruction well-posed, conventional compressed sensing (CS) incorporates prior information about the inherent low dimensionality of images by means of sparsity regularization in a proper transform domain such as Wavelet (WV), or, finite differences (or Total Variation, TV) [9],”
AMP-Net: Denoising-Based Deep Unfolding for Compressive Image Sensing (2020, background): “It has been proved that combining multiple kinds of image prior knowledges can get better reconstruction results than single one [11], [12], [42].”
Deep-Learning Methods for Parallel Magnetic Resonance Imaging Reconstruction: A Survey of the Current Approaches, Trends, and Issues (2019, methodology): “been used successfully in combination with radial [19] and spiral [28] acquisitions as well as in dynamic imaging [29]. More advanced regularizers based on low-rank properties have also been utilized [30]. Figure 3 shows an example of a nonlinear combined parallel imaging and compressed sensing reco”