Modeling and correction of artifacts due to z-motion in 2-D MRI

In 2D Fourier magnetic resonance imaging (MRI), patient motion, including respiratory, cardiac, and involuntary motion, plays a significant role in degradation of the image quality. The in-plane motion (x-y motion) results only in phase distortions in the raw (Fourier domain) MRI data, which can be easily corrected once the motion kernel is known. However, the effect of motion in the slice-selection direction (z-motion) has not yet been completely analyzed due to its significantly more complex nature. The authors propose a novel model to represent the effect of z-motion in the data acquisition process, and then develop two postprocessing methods for the correction of z-motion artifacts provided that the z-motion kernel is known. The model takes the form of a multi-input single-output, shift-variant system. Thus, the inversion of this system is treated by using some nonlinear methods such as the projection onto convex sets (POCS) technique and a Monte Carlo method