Deconvolution‐based distortion correction of EPI using analytic single‐voxel point‐spread functions
Franz Patzig, Toralf Mildner, Torsten Schlumm, Roland Müller, Harald E. Möller
Abstract
Purpose
To develop a postprocessing algorithm that corrects geometric distortions due to spatial variations of the static magnetic field amplitude, B 0, and effects from relaxation during signal acquisition in EPI.
Theory and Methods
An analytic, complex point‐spread function is deduced for k‐space trajectories of EPI variants and applied to corresponding acquisitions in a resolution phantom and in human volunteers at 3 T. With the analytic point‐spread function and experimental maps of B 0 (and, optionally, the effective transverse relaxation time, 
) as input, a point‐spread function matrix operator is devised for distortion correction by a Thikonov‐regularized deconvolution in image space. The point‐spread function operator provides additional information for an appropriate correction of the signal intensity distribution. A previous image combination algorithm for acquisitions with opposite phase blip polarities is adapted to the proposed method to recover destructively interfering signal contributions.
Results
Applications of the proposed deconvolution‐based distortion correction (“DecoDisCo”) algorithm demonstrate excellent distortion corrections and superior performance regarding the recovery of an undistorted intensity distribution in comparison to a multifrequency reconstruction. Examples include full and partial Fourier standard EPI scans as well as double‐shot center‐out trajectories. Compared with other distortion‐correction approaches, DecoDisCo permits additional deblurring to obtain sharper images in cases of significant effects.
Conclusion
Robust distortion corrections in EPI acquisitions are feasible with high quality by regularized deconvolution with an analytic point‐spread function. The general algorithm, which is publicly released on GitHub, can be straightforwardly adapted for specific EPI variants or other acquisition schemes.