Accelerated Cardiac Diffusion Tensor Imaging Using Joint Low-Rank and Sparsity Constraints

Objective: The purpose of this manuscript is to accelerate cardiac diffusion tensor imaging (CDTI) by integrating low-rankness and compressed sensing. Methods: Diffusion-weighted images exhibit both transform sparsity and low-rankness. These properties can jointly be exploited to accelerate CDTI, especially when a phase map is applied to correct for the phase inconsistency across diffusion directions, thereby enhancing low-rankness. The proposed method is evaluated both ex vivo and in vivo, and is compared to methods using either a low-rank or sparsity constraint alone. Results: Compared to using a low-rank or sparsity constraint alone, the proposed method preserves more accurate helix angle features, the transmural continuum across the myocardium wall, and mean diffusivity at higher acceleration, while yielding significantly lower bias and higher intraclass correlation coefficient. Conclusion: Low-rankness and compressed sensing together facilitate acceleration for both ex vivo and in vivo CDTI, improving reconstruction accuracy compared to employing either constraint alone. Significance: Compared to previous methods for accelerating CDTI, the proposed method has the potential to reach higher acceleration while preserving myofiber architecture features which may allow more spatial coverage, higher spatial resolution and shorter temporal footprint in the future.Comment: 11 pages, 16 figures, published on IEEE Transactions on Biomedical Engineerin

Low-rank Tensor Assisted K-space Generative Model for Parallel Imaging Reconstruction

Although recent deep learning methods, especially generative models, have shown good performance in fast magnetic resonance imaging, there is still much room for improvement in high-dimensional generation. Considering that internal dimensions in score-based generative models have a critical impact on estimating the gradient of the data distribution, we present a new idea, low-rank tensor assisted k-space generative model (LR-KGM), for parallel imaging reconstruction. This means that we transform original prior information into high-dimensional prior information for learning. More specifically, the multi-channel data is constructed into a large Hankel matrix and the matrix is subsequently folded into tensor for prior learning. In the testing phase, the low-rank rotation strategy is utilized to impose low-rank constraints on tensor output of the generative network. Furthermore, we alternately use traditional generative iterations and low-rank high-dimensional tensor iterations for reconstruction. Experimental comparisons with the state-of-the-arts demonstrated that the proposed LR-KGM method achieved better performance

Alternating Deep Low Rank Approach for Exponential Function Reconstruction and Its Biomedical Magnetic Resonance Applications

Exponential function is a fundamental signal form in general signal processing and biomedical applications, such as magnetic resonance spectroscopy and imaging. How to reduce the sampling time of these signals is an important problem. Sub-Nyquist sampling can accelerate signal acquisition but bring in artifacts. Recently, the low rankness of these exponentials has been applied to implicitly constrain the deep learning network through the unrolling of low rank Hankel factorization algorithm. However, only depending on the implicit low rank constraint cannot provide the robust reconstruction, such as sampling rate mismatches. In this work, by introducing the explicit low rank prior to constrain the deep learning, we propose an Alternating Deep Low Rank approach (ADLR) that utilizes deep learning and optimization solvers alternately. The former solver accelerates the reconstruction while the latter one corrects the reconstruction error from the mismatch. The experiments on both general exponential functions and realistic biomedical magnetic resonance data show that, compared with the state-of-the-art methods, ADLR can achieve much lower reconstruction error and effectively alleviates the decrease of reconstruction quality with sampling rate mismatches.Comment: 14 page

Self-Learned Kernel Low Rank Approach TO Accelerated High Resolution 3D Diffusion MRI

Diffusion Magnetic Resonance Imaging (dMRI) is a promising method to analyze the subtle changes in the tissue structure. However, the lengthy acquisition time is a major limitation in the clinical application of dMRI. Different image acquisition techniques such as parallel imaging, compressed sensing, has shortened the prolonged acquisition time but creating high-resolution 3D dMRI slices still requires a significant amount of time. In this study, we have shown that high resolution 3D dMRI can be reconstructed from the highly undersampled k-space and q-space data using a Kernel Low Rank method. Our proposed method has outperformed the conventional CS methods in terms of both image quality and diffusion maps constructed from the diffusion-weighted images

Self-Learned Kernel Low Rank Approach TO Accelerated High Resolution 3D Diffusion MRI

Diffusion Magnetic Resonance Imaging (dMRI) is a promising method to analyze the subtle changes in the tissue structure. However, the lengthy acquisition time is a major limitation in the clinical application of dMRI. Different image acquisition techniques such as parallel imaging, compressed sensing, has shortened the prolonged acquisition time but creating high-resolution 3D dMRI slices still requires a significant amount of time. In this study, we have shown that high resolution 3D dMRI can be reconstructed from the highly undersampled k-space and q-space data using a Kernel Low Rank method. Our proposed method has outperformed the conventional CS methods in terms of both image quality and diffusion maps constructed from the diffusion-weighted images