| Inversion techniques are widely used in parallel imaging, where the effect of coil sensitivities and aliasing are unfolded from the multichannel observations. These techniques require knowledge of coil sensitivities. As a common method, a low-pass approximation of the true spin density function is obtained first and then coil sensitivities are calculated by removing the effect of the true image from the coil images. This approximation is conventionally either obtained directly from a body-coil or from a coil combined image, for example calculated using square-root sum-of squares (SoS) combination approach. However, acquiring a body coil image increases the data acquisition time and also can be sensitive to motion and B0 field inhomogeneities. On the other hand, SoS combination gives biased and low-contrast images. In this dissertation, subspace concepts are shown to be effective to obtain an estimate of coil sensitivities in k-space. From there, it is possible to extract the calibration kernels of the coil-by-coil reconstruction methods such as GRAPPA, SPIRiT and PRUNO using the explicit formulas given in this dissertation. As a result, this formulation provides a unified framework for the inversion and the coil-by-coil interpolation reconstruction techniques.;Coil sensitivities or calibration kernels of parallel imaging algorithms are conventionally extracted from a region of fully sampled low-pass calibration data. However, for high acceleration rates, the acquisition of the fully sampled calibration data becomes a limiting factor. Thus, we also investigate extraction of coil sensitivities and calibration kernels from subsampled reference or ACS lines. We present a non-iterative, subspace-based approach to the recovery of the coil sensitivity functions from a nonuniform periodically sampled auto-calibration signal (ACS) region of k-space, providing flexibility to balance high-frequency detail with low-frequency signal strength. The non-iterative algorithm has low computational complexity, consistent with clinically relevant reconstruction times. A system theoretic analysis provides a proof of uniqueness of coil sensitivities for a special class of non-uniform periodic sampling.;For parallel MRI, interpolation techniques such as GRAPPA are widely employed due to fast computation times and robust image reconstruction. GRAPPA reconstruction, however, suffers from noise amplification, especially at high acceleration rates. We propose a pre-processing approach to suppress noise by exploiting structure in matrices obtained from fully sampled and uniformly subsampled acquired data. In particular, Hankel-block-Hankel and low-rank properties are jointly enforced on linear operators constructed from acquired k-space data. By itself, the proposed pre-processing technique provides 1-6 dB enhancement in peak and average signal-to-noise ratio (SNR) without amplifying artifacts or introducing blurring. When used in conjunction with existing post-processing methods, e.g., total variation denoising or non-local means filtering, the proposed method yields 3-14 dB improvement in peak and average SNR.;In preliminary work, we also use subspace techniques for coil combination once the interpolated k-space data are obtained using coil-by-coil reconstruction techniques such as GRAPPA. Intriguing empirical results with simulated and in vivo data show that the ad hoc technique results in images that exhibit less bias and higher contrast than the existing approaches, such as SoS. Theoretical justification and connection to principled estimation procedures remain ongoing work. (Abstract shortened by UMI.). |
