Bi-Linear Modeling of Data Manifolds for Dynamic-MRI Recovery
IEEE TRANSACTIONS ON MEDICAL IMAGING
2020; 39 (3): 688–702
This paper puts forth a novel bi-linear modeling framework for data recovery via manifold-learning and sparse-approximation arguments and considers its application to dynamic magnetic-resonance imaging (dMRI). Each temporal-domain MR image is viewed as a point that lies onto or close to a smooth manifold, and landmark points are identified to describe the point cloud concisely. To facilitate computations, a dimensionality reduction module generates low-dimensional/compressed renditions of the landmark points. Recovery of high-fidelity MRI data is realized by solving a non-convex minimization task for the linear decompression operator and affine combinations of landmark points which locally approximate the latent manifold geometry. An algorithm with guaranteed convergence to stationary solutions of the non-convex minimization task is also provided. The aforementioned framework exploits the underlying spatio-temporal patterns and geometry of the acquired data without any prior training on external data or information. Extensive numerical results on simulated as well as real cardiac-cine MRI data illustrate noteworthy improvements of the advocated machine-learning framework over state-of-the-art reconstruction techniques.
View details for DOI 10.1109/TMI.2019.2934125
View details for Web of Science ID 000525262100014
View details for PubMedID 31403408
Acceleration of three-dimensional diffusion magnetic resonance imaging using a kernel low-rank compressed sensing method.
Diffusion Magnetic Resonance Imaging (dMRI) has shown great potential in probing tissue microstructure and structural connectivity in the brain but is often limited by the lengthy scan time needed to sample the diffusion profile by acquiring multiple diffusion weighted images (DWIs). Although parallel imaging technique has improved the speed of dMRI acquisition, attaining high resolution three dimensional (3D) dMRI on preclinical MRI systems remained still time consuming. In this paper, kernel principal component analysis, a machine learning approach, was employed to estimate the correlation among DWIs. We demonstrated the feasibility of such correlation estimation from low-resolution training DWIs and used the correlation as a constraint to reconstruct high-resolution DWIs from highly under-sampled k-space data, which significantly reduced the scan time. Using full k-space 3D dMRI data of post-mortem mouse brains, we retrospectively compared the performance of the so-called kernel low rank (KLR) method with a conventional compressed sensing (CS) method in terms of image quality and ability to resolve complex fiber orientations and connectivity. The results demonstrated that the KLR-CS method outperformed the conventional CS method for acceleration factors up to 8 and was likely to enhance our ability to investigate brain microstructure and connectivity using high-resolution 3D dMRI.
View details for DOI 10.1016/j.neuroimage.2020.116584
View details for PubMedID 32004717
KerNL: Kernel-Based Nonlinear Approach to Parallel MRI Reconstruction
IEEE TRANSACTIONS ON MEDICAL IMAGING
2019; 38 (1): 312–21
The conventional calibration-based parallel imaging method assumes a linear relationship between the acquired multi-channel k-space data and the unacquired missing data, where the linear coefficients are estimated using some auto-calibration data. In this paper, we first analyze the model errors in the conventional calibration-based methods and demonstrate the nonlinear relationship. Then, a much more general nonlinear framework is proposed for auto-calibrated parallel imaging. In this framework, kernel tricks are employed to represent the general nonlinear relationship between acquired and unacquired k-space data without increasing the computational complexity. Identification of the nonlinear relationship is still performed by solving linear equations. Experimental results demonstrate that the proposed method can achieve reconstruction quality superior to GRAPPA and NL-GRAPPA at high net reduction factors.
View details for DOI 10.1109/TMI.2018.2864197
View details for Web of Science ID 000455110500030
View details for PubMedID 30106676
View details for PubMedCentralID PMC6422679
MLS: Joint Manifold-Learning and Sparsity-Aware Framework for Highly Accelerated Dynamic Magnetic Resonance Imaging
IEEE. 2018: 1213–16
Manifold-based models have been recently exploited for accelerating dynamic magnetic resonance imaging (dMRI). While manifold-based models have shown to be more efficient than conventional low-rank approaches, joint low-rank and sparsity-aware modeling still appears to be very efficient due to the inherent sparsity within dMR images. In this paper, we propose a joint manifold-learning and sparsity-aware framework for dMRI. The proposed method establishes a link between the recently developed manifold models and conventional sparsity-aware models. Dynamic MR images are modeled as points located on or close to a smooth manifold, and a novel data-driven manifold-learning approach, which preserves affine relation among images, is used to learn the low-dimensional embedding of the dynamic images. The temporal basis learnt from such an approach efficiently captures the inherent periodicity of dynamic images and hence sparsity along temporal direction is enforced during reconstruction. The proposed framework is validated by extensive numerical tests on phantom and in-vivo data sets.
View details for Web of Science ID 000455045600278
View details for PubMedID 31007840
View details for PubMedCentralID PMC6469692
Bi-Linear Modeling of Manifold-Data Geometry for Dynamic-MRI Recovery.
... International Workshop on Computational Advances in Multi-Sensor Adaptive Processing. International Workshop on Computational Advances in Multi-Sensor Adaptive Processing
This paper establishes a modeling framework for data located onto or close to (unknown) smooth manifolds, embedded in Euclidean spaces, and considers its application to dynamic magnetic resonance imaging (dMRI). The framework comprises several modules: First, a set of landmark points is identified to describe concisely a data cloud formed by highly under-sampled dMRI data, and second, low-dimensional renditions of the landmark points are computed. Searching for the linear operator that decompresses low-dimensional data to high-dimensional ones, and for those combinations of landmark points which approximate the manifold data by affine patches, leads to a bi-linear model of the dMRI data, cognizant of the intrinsic data geometry. Preliminary numerical tests on synthetically generated dMRI phantoms, and comparisons with state-of-the-art reconstruction techniques, underline the rich potential of the proposed method for the recovery of highly under-sampled dMRI data.
View details for DOI 10.1109/CAMSAP.2017.8313115
View details for PubMedID 31763626
A Kernel-Based Low-Rank (KLR) Model for Low-Dimensional Manifold Recovery in Highly Accelerated Dynamic MRI
IEEE TRANSACTIONS ON MEDICAL IMAGING
2017; 36 (11): 2297–2307
While many low rank and sparsity-based approaches have been developed for accelerated dynamic magnetic resonance imaging (dMRI), they all use low rankness or sparsity in input space, overlooking the intrinsic nonlinear correlation in most dMRI data. In this paper, we propose a kernel-based framework to allow nonlinear manifold models in reconstruction from sub-Nyquist data. Within this framework, many existing algorithms can be extended to kernel framework with nonlinear models. In particular, we have developed a novel algorithm with a kernel-based low-rank model generalizing the conventional low rank formulation. The algorithm consists of manifold learning using kernel, low rank enforcement in feature space, and preimaging with data consistency. Extensive simulation and experiment results show that the proposed method surpasses the conventional low-rank-modeled approaches for dMRI.
View details for DOI 10.1109/TMI.2017.2723871
View details for Web of Science ID 000414134200010
View details for PubMedID 28692970
View details for PubMedCentralID PMC6422674
M-MRI: A Manifold-based Framework to Highly Accelerated Dynamic Magnetic Resonance Imaging
IEEE. 2017: 19–22
High-dimensional signals, including dynamic magnetic resonance (dMR) images, often lie on low dimensional manifold. While many current dynamic magnetic resonance imaging (dMRI) reconstruction methods rely on priors which promote low-rank and sparsity, this paper proposes a novel manifold-based framework, we term M-MRI, for dMRI reconstruction from highly undersampled k-space data. Images in dMRI are modeled as points on or close to a smooth manifold, and the underlying manifold geometry is learned through training data, called "navigator" signals. Moreover, low-dimensional embeddings which preserve the learned manifold geometry and effect concise data representations are computed. Capitalizing on the learned manifold geometry, two regularization loss functions are proposed to reconstruct dMR images from highly undersampled k-space data. The advocated framework is validated using extensive numerical tests on phantom and in-vivo data sets.
View details for Web of Science ID 000414283200005
View details for PubMedID 30956752
View details for PubMedCentralID PMC6449852
- Highly Accelerated Cardiac Cine parallel MRI using Low-Rank Matrix Completion and Partial Separability Model SPIE-INT SOC OPTICAL ENGINEERING. 2016
ACCELERATING DYNAMIC MAGNETIC RESONANCE IMAGING BY NONLINEAR SPARSE CODING
IEEE. 2016: 510–13
Although being high-dimensional, dynamic magnetic resonance images usually lie on low-dimensional manifolds. Nonlinear models have been shown to capture well that latent low-dimensional nature of data, and can thus lead to improvements in the quality of constrained recovery algorithms. This paper advocates a novel reconstruction algorithm for dynamic magnetic resonance imaging (dMRI) based on nonlinear dictionary learned from low-spatial but high-temporal resolution images. The nonlinear dictionary is initially learned using kernel dictionary learning, and the proposed algorithm subsequently alternates between sparsity enforcement in the feature space and the data-consistency constraint in the original input space. Extensive numerical tests demonstrate that the proposed scheme is superior to popular methods that use linear dictionaries learned from the same set of training data.
View details for Web of Science ID 000386377400122
View details for PubMedID 31709030
View details for PubMedCentralID PMC6839784
DYNAMIC MAGNETIC RESONANCE IMAGING USING COMPRESSED SENSING WITH SELF-LEARNED NONLINEAR DICTIONARY (NL-D)
IEEE. 2015: 331–34
View details for Web of Science ID 000380546000079