Second-Order TGV Reconstruction for Undersampled Radial MRI

Total generalized variation for denoising and reconstruction of accelerated MR data.

We are sharing MATLAB reconstruction code for undersampled radial MR data with a second-order total generalized variation (TGV) constraint and a primal dual extragradient method.

We proposed TGV as a generalization of the total variation theory. As a penalty term for MRI problems, TGV preserves the benefits of previously introduced total variation (TV) without being bound by the limitations inherent in the assumptions that underlie TV.

For more details, see the related publication.

Related Publication

Knoll F, Bredies K, Pock T, Stollberger R.
Second order total generalized variation (TGV) for MRI.
Magn Reson Med. 2011 Feb;65(2):480-91. doi: 10.1002/mrm.22595

Please cite this work if you are using second-order TGV reconstruction in your research.

Get the Code

The software available on this page is provided free of charge and comes without any warranty. CAI²R and NYU Grossman School of Medicine do not take any liability for problems or damage of any kind resulting from the use of the files provided. Operation of the software is solely at the user’s own risk. The software developments provided are not medical products and must not be used for making diagnostic decisions.

The software is provided for non-commercial, academic use only. Usage or distribution of the software for commercial purpose is prohibited. All rights belong to the author (Florian Knoll) and NYU Grossman School of Medicine. If you use the software for academic work, please give credit to the author in publications and cite the related publications.

Please spell out your affiliation (e.g. “New York University” rather than “NYU”).


Questions about this resource may be directed to Florian Knoll, PhD.

Related Resource

Elsewhere on this site, we are sharing AGILE, a more efficient GPU implementation for linear and non-linear image reconstruction.