An inverse problem approach to the correction of distortion in EPI images

Magnetic resonance imaging using the echo planar imaging (EPI) technique is particularly sensitive to main (B ₀) field inhomogeneities. The primary effect is geometrical distortion in the phase encoding direction. Here, the authors present a method based on the conjugate gradient algorithm to correct for this geometrical distortion, by solving the EPI imaging equation. Two versions are presented: one that attempts to solve the full four-dimensional (4-D) imaging equation, and one that independently solves for each profile along the blip encoding direction. Results are presented for both phantom and in vivo brain EPI images and compared with other proposed correction methods.