A Study of Nonlinear Approaches to Parallel Magnetic Resonance Imaging

Magnetic resonance imaging (MRI) has revolutionized radiology in the past four decades by its ability to visualize not only the detailed anatomical structures, but also function and metabolism information. A major limitation with MRI is its low imaging speed, which makes it difficult to image the moving objects. Parallel MRI (pMRI) is an emerging technique to increase the speed of MRI. It acquires the MRI data from multiple coils simultaneously such that fast imaging can be achieved by reducing the amount of data acquired in each coil. Several methods have developed to reconstruct the original image using the reduced data from multiple coils based on their distinct spatial sensitivities. Among the existing methods, Sensitivity Encoding (SENSE) and GeneRally Autocalibrating Partially Parallel Acquisition (GRAPPA) are commercially used reconstruction methods for parallel MRI. Both methods use linear approaches for image reconstruction. GRAPPA is known to outperform SENSE because no coil sensitivities are needed in reconstruction. However, GRAPPA can only accelerate the speed by a factor of 2-3. The objective of this dissertation is to develop novel techniques to significantly improve the acceleration factor upon the existing GRAPPA methods. Motivated by the success of recent study in our group which has demonstrated the benefit of nonlinear approaches for SENSE, in this dissertation, nonlinear approaches are studied for GRAPPA. Based on the fact that GRAPPA needs a calibration step before reconstruction, nonlinear models are investigated in both calibration and reconstruction using a kernel method widely used in machine learning. In addition, compressed sensing (CS), a nonlinear optimization technique will also be incorporated for even higher accelerations. In order to reduce the computation time, a nonlinear approach is proposed to reduce the effective number of coils in reconstruction. The imaging speed is expected to improve by a factor of 4-6 using the proposed nonlinear techniques. These new techniques will find many applications in accurate brain imaging, dynamic cardiac imaging, functional imaging, and so forth

Parallel Magnetic Resonance Imaging as Approximation in a Reproducing Kernel Hilbert Space

In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial frequency domain (k-space), typically by time-consuming line-by-line scanning on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of data using multiple receivers (parallel imaging), and by using more efficient non-Cartesian sampling schemes. As shown here, reconstruction from samples at arbitrary locations can be understood as approximation of vector-valued functions from the acquired samples and formulated using a Reproducing Kernel Hilbert Space (RKHS) with a matrix-valued kernel defined by the spatial sensitivities of the receive coils. This establishes a formal connection between approximation theory and parallel imaging. Theoretical tools from approximation theory can then be used to understand reconstruction in k-space and to extend the analysis of the effects of samples selection beyond the traditional g-factor noise analysis to both noise amplification and approximation errors. This is demonstrated with numerical examples.Comment: 28 pages, 7 figure

Accelerated Coronary MRI with sRAKI: A Database-Free Self-Consistent Neural Network k-space Reconstruction for Arbitrary Undersampling

This study aims to accelerate coronary MRI using a novel reconstruction algorithm, called self-consistent robust artificial-neural-networks for k-space interpolation (sRAKI). sRAKI performs iterative parallel imaging reconstruction by enforcing coil self-consistency using subject-specific neural networks. This approach extends the linear convolutions in SPIRiT to nonlinear interpolation using convolutional neural networks (CNNs). These CNNs are trained individually for each scan using the scan-specific autocalibrating signal (ACS) data. Reconstruction is performed by imposing the learned self-consistency and data-consistency enabling sRAKI to support random undersampling patterns. Fully-sampled targeted right coronary artery MRI was acquired in six healthy subjects for evaluation. The data were retrospectively undersampled, and reconstructed using SPIRiT, $\ell_1$-SPIRiT and sRAKI for acceleration rates of 2 to 5. Additionally, prospectively undersampled whole-heart coronary MRI was acquired to further evaluate performance. The results indicate that sRAKI reduces noise amplification and blurring artifacts compared with SPIRiT and $\ell_1$-SPIRiT, especially at high acceleration rates in targeted data. Quantitative analysis shows that sRAKI improves normalized mean-squared-error (~44% and ~21% over SPIRiT and $\ell_1$-SPIRiT at rate 5) and vessel sharpness (~10% and ~20% over SPIRiT and $\ell_1$-SPIRiT at rate 5). In addition, whole-heart data shows the sharpest coronary arteries when resolved using sRAKI, with 11% and 15% improvement in vessel sharpness over SPIRiT and $\ell_1$-SPIRiT, respectively. Thus, sRAKI is a database-free neural network-based reconstruction technique that may further accelerate coronary MRI with arbitrary undersampling patterns, while improving noise resilience over linear parallel imaging and image sharpness over $\ell_1$ regularization techniques.Comment: This work has been partially presented at ISMRM Workshop on Machine Learning Part 2 (October 2018), SCMR/ISMRM Co-Provided Workshop (February 2019), IEEE International Symposium on Biomedical Imaging (April 2019) and ISMRM 27$^{th}$ Annual Meeting and Exhibition (May 2019