Automatic suppression of spatially variant translational motion artifacts in magnetic resonance imaging

This paper summarizes the theory of a novel post-processing approach to automatic motion artifact suppression in magnetic resonance imaging. The main advantage of the new approach is its treatment of practical spatially variant translational motion model that is fundamentally different from previous work in the literature. We first consider a 1-D model for the problem based on differentiated rather than original image. In this model, the motion artifact amounts to blurring of peaks corresponding to the edges in the original image. Observing that the distorted and true images share the same 2-norm, we search for the true image on the hyper-sphere with radius equal to this norm. We show that the solution must have the minimum 1-norm of all vectors on the hyper-sphere and a search strategy based on dynamic programming is used to estimate the motion at a reasonable complexity. Subsequently, this procedure is applied to different regions in the image independently and spatially variant motion model parameters are derived at a resolution of the region sizes. Finally, we show the similarity between this problem and the problem of magnetic field inhomogeneity distortion. Based on this similarity, an image reconstruction strategy and an expression for the point-spread function of the resultant image are derived. The new technique is applied to correct computer simulated images and promising results are obtained