Subspace estimation for subspace-based magnetic resonance spectroscopic imaging

Magnetic resonance spectroscopic imaging (MRSI) is a powerful technique that offers us the ability to non-invasively image chemical distributions within the human body. However, due to its inherently poor trade-off between imaging speed, resolution, and signal-to-noise ratio (SNR), MRSI has remained impractical for many research and clinical applications. A large body of work has been done to improve this trade-off. Recently new subspace-based imaging methods have also been proposed as a means of dramatically accelerating MRSI. By taking advantage of the properties of a partially separable (PS) signal model, subspace-based methods offer increased flexibility in acquisition as well as image reconstruction, and thereby allow high-resolution, high-SNR MRSI images to be obtained in a fraction of the time required by standard techniques. An important ingredient common to all subspace-based imaging methods is the estimation of the subspace structure of the high-dimensional image function. However, accurate subspace estimation in the presence of noise and inhomogeneity in the main magnetic field is challenging. To this end we propose a novel method for subspace estimation which utilizes a regularized-reconstruction approach to correct for the effects of field inhomogeneity and noise. Carefully designed numerical simulations and experimental studies have been performed to evaluate the performance of the proposed method in a variety of experimental conditions. Results from these data show that the proposed method is able to obtain an accurate subspace estimation, either in terms of a projection error metric or by inspecting the residual after projecting the fully sampled data onto the estimated subspaces. Additionally, in vivo MRSI data was acquired to illustrate that the subspace estimated by the proposed method leads to high-quality spatiospectral reconstructions