Advanced image reconstruction in parallel magnetic resonance imaging : constraints and solutions.

Abstract

Imaging speed is a crucial consideration for magnetic resonance imaging (MRI). The speed of conventional MRI is limited by hardware performance and physiological safety measures. "Parallel" MRI is a new technique that circumvents these limitations by utilizing arrays of radiofrequency detector coils to acquire data in parallel, thereby enabling still higher imaging speeds. In parallel MRI, coil arrays are used to accomplish part of the spatial encoding that was traditionally performed by magnetic field gradients alone. MR signal data acquired with coil arrays are spatially encoded with the distinct reception patterns of the individual coil elements. T[he quality of parallel MR images is dictated by the accuracy and efficiency of an image reconstruction (decoding) strategy. This thesis formulates the spatial encoding and decoding of parallel MRI as a generalized linear inverse problem. Under this linear algebraic framework, theoretical and empirical limits on the performance of parallel MR image reconstructions are characterized, and solutions are proposed to facilitate routine clinical and research applications. Each research study presented in this thesis addresses one or more elements in the inverse problem, and the studies are collectively arranged to reflect three progressive stages in solving the inverse problem: 1) determining the encoding matrix, 2) computing a matrix inverse, 3) characterizing the error involved. First, a self-calibrating strategy is proposed which uses non-Cartesian trajectories to automatically determine coil sensitivities without the need of an external scan or modification of data acquisition, guaranteeing an accurate formulation of the encoding matrix.

(cont.) Second, two matrix inversion strategies are presented which, respectively, exploit physical properties of coil encoding and the phase information of the magnetization. While the former allows stable and distributable matrix inversion using the k-space locality principle, the latter integrates parallel image reconstruction with conjugate symmetry. Third, a numerical strategy is presented for computing noise statistics of parallel MRI techniques which involve magnitude image combination, enabling quantitative image comparison. In addition, fundamental limits on the performance of parallel image reconstruction are derived using the Cramer-Rao bounds. Lastly, the practical applications of techniques developed in this thesis are demonstrated by a case study in improved coronary angiography.