Accelerating magnetic resonance imaging by unifying sparse models and multiple receivers

Abstract

Magnetic resonance imaging (MRI) is an increasingly versatile diagnostic tool for a variety of medical purposes. During a conventional MRI scan, samples are acquired along a trajectory in the spatial Fourier transform domain (called k-space) and the image is reconstructed using an inverse discrete Fourier transform. The affordability, availability, and applications of MRI remain limited by the time required to sample enough points of k-space for the desired field of view (FOV), resolution, and signal-to-noise ratio (SNR). GRAPPA, an accelerated parallel imaging method, and compressed sensing (CS) have been successfully employed to accelerate the acquisition process by reducing the number of k-space samples required. GRAPPA leverages the different spatial weightings of each receiver coil to undo the aliasing from the reduction in FOV induced by undersampling k-space. However, accelerated parallel imaging reconstruction methods like GRAPPA amplify the noise present in the data, reducing the SNR by a factor greater than that due to only the level of undersampling. Completely separate from accelerated parallel imaging, which capitalizes on observing data with multiple receivers, CS leverages the sparsity of the object along with incoherent sampling and nonlinear reconstruction algorithms to recover the image from fewer samples. In contrast to parallel imaging, CS actually denoises the result, because noise typically is not sparse. When reconstructing brain images, the discrete wavelet transform and finite differences are effective in producing an approximately sparse representation of the image. Because parallel imaging utilizes the multiple receiver coils and CS takes advantage of the sparsity of the image itself, these methods are complementary, and a combination of these methods would be expected to enable further acceleration beyond what is achievable using parallel imaging or CS alone. This thesis investigates three approaches to leveraging both multiple receiver coils and image sparsity. The first approach involves an optimization framework for jointly optimizing the fidelity to the GRAPPA result and the sparsity of the image. This technique operates in the nullspace of the data observation matrix, preserving the acquired data without resorting to techniques for constrained optimization. While this framework is presented generally, the effectiveness of the implementation depends on the choice of sparsifying transform, sparsity penalty function, and undersampling pattern. The second approach involves modifying the kernel estimation step of GRAPPA to promote sparsity in the reconstructed image and mitigate the noise amplification typically encountered with parallel imaging. The third approach involves imposing a sparsity prior on the coil images and estimating the full k-space from the observations using Bayesian techniques. This third method is extended to jointly estimate the GRAPPA kernel weights and the full k-space together. These approaches represent different frameworks for accelerating MRI imaging beyond current methods. The results presented suggest that these practical reconstruction and post-processing methods allow for greater acceleration with conventional Cartesian acquisitions.