Referenceless Nyquist Ghost Correction Source Code

You are here

Referenceless Nyquist Ghost Correction for Echo Planar Imaging (EPI)

EPI is subject to Nyquist (or N/2) ghosts caused by eddy currents, imperfect gradients, and/or timing errors. Nyquist ghosts are typically corrected using a 3-line navigator to measure the 1st-order phase difference [1]. However, several alternative ghost correction strategies can estimate the 1st-order correction parameters using a cost function calculated on the data itself, rather than any reference acquisition. One method is Ghost/Object (G/O) minimization [2], which defines the cost function as the summation over the entire image divided by a ½-FOV-shifted version of the image.


A demonstration of the algorithm is provided in Matlab format, available for download here.

The code provided here demonstrates 1st-order ghost correction using G/O minimization and has the option to test other referenceless methods (entropy [3,4], SVD [5], image energy). The optimization can be done using a discrete or simplex search.

For commercial licensing inquiries, please see this link:

Copyright & License Notice
This software is copyrighted by the Regents of the University of Minnesota. It can be freely used for educational and research purposes by non-profit institutions and US government agencies only. Other organizations are allowed to use this software only for evaluation purposes, and any further uses will require prior approval. The software may not be sold or redistributed without prior approval. One may make copies of the software for their use provided that the copies, are not sold or distributed, are used under the same terms and conditions.

As unestablished research software, this code is provided on an "as is'' basis without warranty of any kind, either expressed or implied. The downloading, or executing any part of this software constitutes an implicit agreement to these terms. These terms and conditions are subject to change at any time without prior notice.


  • [1] Heid, O. Method for the phase correction of nuclear magnetic resonance signals. US Patent 6,043,651. 2000.
  • [2] McKay JA, Moeller S, Zhang L, Auerbach EJ, Nelson MT, Bolan PJ. Nyquist ghost correction of breast diffusion weighted imaging using referenceless methods. Magn Reson Med. 2019;81:2624–2631.
  • [3] Clare, S. Iterative Nyquist ghost correction for single and multi-shot EPI using an entropy measure. In Proceedings of ISMRM. 2003;p.1041.
  • [4] Skare S, Clayton DB, Newbould R, Moseley M, and Bammer R. A fast and robust minimum entropy based non-interactive Nyquist ghost correction algorithm. In Proceedings of ISMRM. 2006;p.2349.
  • [5] Peterson E, Aksoy M, Maclaren J, and Bammer R. Acquisition-free Nyquist ghost correction for parallel imaging accelerated EPI. In Proceedings of ISMRM. 2015;p.0075.