Rapid Magnetic Resonance Imaging Using Random Projection, Nonlinear Kernel, and Compressed Sensing
Lv (Lyu), Jingyuan
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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. The conventional calibration-based parallel imaging method assumes a linear relationship between the acquired undersampled k-space data and the unacquired missing k-space data, where the linear coefficients are estimated using some auto-calibration data. In this work, we have proposed a nonvel nonlinear kernel approach to 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. Besides, we propose a random projection approach to further accelerate the reconstruction process of parallel MRI. In addition, we have proposed a new formulation for calibration-free reconstruction using Multi-Channel MRI Using Blind De-Convolution, named MALBEC. The method formulates the reconstruction problem as a low-rank matrix recovery problem, but the constraint is stronger than the existing SAKE method. Therefore, the proposed MALBEC method is expected to provide better reconstruction of the image. We have also proposed an approach to reconstruct highly undersampled dynamic MRI with high spatial and temporal resolution. The approach effectively exploits locally low rankness within the navigator region to recover the full from undersampled navigator data, and combines PS with the sparsity constraint and GRAPPA in the same framework.