Reconstruction of MRI Images from Non-Uniform Sampling and Its Application to Intrascan Motion Correction in Functional MRI

Abstract

16.1 Introduction Motion constitutes a perennial problem in Magnetic Resonance Imaging (MRI). It leads to artifacts in the images. In functional MRI (fMRI), motion is also a major limitation to accurate detection of neuronal activity. MRI signals, encoded by a combination of magnetic fields, are sampled in the multi-dimensional k-space. Reconstruction of the MR image from the samples entails transformation from k-space to image space. To help appreciate MRI sampling strategies, Section 16.2 provides an elementary treatment of some basic MRI principles. Section 16.3 deals with motion problems which are a limiting factor for accurate brain activation analysis. A postprocessing method to reduce artifacts arising from motion between measurement of successive "k-space trajectories" is reported. It should be realized that in this case sample positions are pseudorandom. Section 16.4 concerns image reconstruction from non-uniform sample position distribu-tions through gridding. It needs recalculation of sample values from a non-uniform grid to a uniform rectangular grid, entailing correction for variable sampling density. Then, Bayesian estimation (reconstruction) of images from arbitrary sample positions in k-space is presented in Section 16.5. Sec-tion 16.6 treats the applications of the intrascan motion correction method in brain fMRI. Finally, conclusions are drawn in Section 16.7.