Optimal Observation Selection in Magnetic Resonance Spectroscopic Imaging

Abstract

Magnetic resonance spectroscopic imaging (MRSI) is a completely non-invasive method for obtaining quantitative information regarding biochemical parameters [1]. It shows great promise for use in basic physiological research and for clinical imaging of metabolic function [2, 3]. The information obtained with MRSI can be used to assess regional metabolic abnormalities in various pathologies. However, MRSI requires a great deal of time to gather the data necessary to achieve satisfactory resolution. When prior information about the image is available, it may be possible to reconstruct the image from a subset of k-space samples. Therefore, we desire to choose the best possible combination of a small number of k-space samples to guarantee the quality of the reconstructed image by using the available prior knowledge. In this thesis, we assume prior knowledge only of the region of support (ROS) of the spatial-domain image. Sequential forward selection (SFS) is appealing as an optimization method because the previously selected sample can be observed while the next sample is selected. We develop an efficient computational strategy for this algorithm that allows SFS to be applied to this problem when the image region has a known region of support (ROS). The combined algorithm efficiently selects a reduced set of k-space samples from which the ROS can be reconstructed with minimal noise amplification. Furthermore, if there is no noise, the minimum density can be reached with this algorithm. Hexagonal sampling gives a 13.4% sampling density reduction compared to rectangular sampling for images with a circular ROS. However, nonuniform sampling patterns are more efficient than hexagonal sampling for the same ROS. To reduce selection time and achieve higher resolution, we develop a sequential backward selection (SBS) algorithm from samples on a hexagonal grid. Simulation results show that more efficiency and reduced selection time can be achieved with the proposed method in comparison with SBS on a rectangular grid. We develop two efficient algorithms for optimizing the dithering pattern so that an image can be reconstructed as reliably as possible from a periodic nonuniform set of samples, which can be obtained from a dithered rectangular-grid array. One algorithm is SBS of sample arrays. Taking into account the ROS of the image, we sequentially eliminate the least informative array recursively until the minimal number of arrays remain. In this scheme, we provide an efficient update formula for the criterion based on convolution kernels rather than large, non-sparse matrices, an efficient update formula for the convolution kernels based on the deleted array, and an efficient reconstruction method based on convolutions. The proposed method dramatically reduces storage and computational complexity. The other algorithm is SFS of sample arrays. Based on the ROS image, we sequentially select the array that minimizes the noise amplification recursively until the desired number of arrays are selected. To avoid the singularity of the criterion when extending the selection procedure to more samples than unknowns, we propose a modified criterion for the case when the number of unknowns is more than the number of selected samples and the complementary case. We also propose an efficient method to update the criterion based only on the deleted array in the previous step to greatly reduce computational time and avoid the inversion of a huge matrix. This method has great practical potential because it can finish the selection process within half a minute for practical sizes. The proposed schemes in this dissertation efficiently optimize the MRSI observation in different ways. In general, they will reduce observation time and overcome the problems in various available optimization methods.