The authors propose a new method to use a non-linear model for correcting errors in radial trajectories. The model represents shifts of trajectories as a combination of a linear function and a sigmoid function.
Conventional methods assume that the shifts are proportional to the gradient strengths. However, actual trajectories cannot be represented as linear models precisely due to non-linear imperfections of the gradients such as eddy currents.
The proposed method suppresses streak artifacts and image shadings which appear with conventional linear correction.