Application of compressed sensing in quantitative magnetic resonance imaging
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As a powerful quantitative imaging tool for tissue characterizations, MR parameter mapping has demonstrated great potential in various clinical applications. However, one major practical limitation is the long acquisition time. In order to accurately obtain the MR parameters values, a large amount of contrast-weighted images need to be acquired at high resolution. To overcome this issue, in this dissertation, the author proposed three methods to accelerate the MR parameter mapping acquisition. Firstly, we propose a novel reconstruction framework to recover the parameter-weighted images from highly undersampled k-spaces where the unknown images are sparsely represented using nonlinear models. Each parameter-weighted image at a specific time point is assumed to lie in a low-dimensional manifold learned from the training images generated by the parametric model. To reconstruct the image series, among infinite number of solutions that satisfy the data consistent constraint, the one that is closest to the manifold is selected as the desired solution. The underlying optimization problem is solved using kernel trick and split Bregman iteration algorithm with spatial and temporal regularizations. The proposed method was evaluated on a set of in-vivo brain T2 mapping data set and shown to superior to the conventional compressed sensing methods. Secondly, the author investigated the feasibility of accelerating the T1-rho quantification in cartilage imaging using k-t LISD, an advanced MRI reconstruction method that combines compressed sensing with novel support detection and JSENSE. Specifically, the author combines an advanced compressed sensing (CS) based reconstruction technique, k-t ISD with locally adaptive support detection, named k-t LISD and an advanced parallel imaging technique, JSENSE, to reconstruct the T1-rho image sequence from undersampled k-space data acquired at different TSLs. The reconstruction process alternates iteratively between compressed sensing for reconstruction the images sequence and JSENSE for sensitivity estimation. Principle component analysis used as the sparsifying transform. At each compressed sensing iteration, a local thresholding function is applied to each principle component to update the support information to be used in the next iteration. The proposed method was validated on six in vivo human T1-rho cartilage datasets acquired from a bi-lateral scan on three healthy volunteers and achieved a fitting error less than 1% which is much less than the 5% in-vivo reproducibility of cartilage T1-rho quantification. Thirdly, a novel kernel-based compressed sensing reconstruction approach is proposed to accelerate the Arterial Spin Labeling (ASL) perfusion MRI. The method represents the image sequence sparsely and adaptively using nonlinear transformations. Such nonlinearity is implemented using the kernel method, which maps the acquired undersampled k-space data onto a high dimensional feature space, then reconstructs the image sequence in the corresponding feature space using the conventional compressed sensing, and finally convert the image sequence back into the original space. Experimental results demonstrate that the proposed method improves the reconstruction quality both quantitatively and qualitatively over the state-of-the-art method where linear transform is used. These new techniques have great potential to accelerate the quantitative MRI without scarifying the accuracy of parameter estimation.