To investigate and remove Gibbs-ringing artifacts caused by partial Fourier (PF) acquisition and zero filling interpolation in MRI data.
Theory and Methods
Gibbs ringing of fully sampled data, leading to oscillations around tissue boundaries, is caused by the symmetric truncation of k-space. Such ringing can be removed by conventional methods, with the local subvoxel shifts method being the state-of-the-art. However, the asymmetric truncation of k-space in routinely used PF acquisitions leads to additional ringings of wider intervals in the PF sampling dimension that cannot be corrected solely based on magnitude images reconstructed via zero filling. Here, we develop a pipeline for the Removal of PF-induced Gibbs ringing (RPG) to remove ringing patterns of different periods by applying the conventional method twice. The proposed pipeline is validated on numerical phantoms, demonstrated on in vivo diffusion MRI measurements, and compared with the conventional method and neural network-based approach.
Results
For PF = 7/8 and 6/8, Gibbs-ringings and subsequent bias in diffusion metrics induced by PF acquisition and zero filling are robustly removed by using the proposed RPG pipeline. For PF = 5/8, however, ringing removal via RPG leads to excessive image blurring due to the interplay of image phase and convolution kernel.
Conclusions
RPG corrects Gibbs-ringing artifacts in magnitude images of PF acquired data and reduces the bias in quantitative MR metrics. Considering the benefit of PF acquisition and the feasibility of ringing removal, we suggest applying PF = 6/8 when PF acquisition is necessary.
I was unaware of the sub-pixel shifting approach. This seems like a meaningful extension of that technique.
It seems like the simplest way to mitigate Gibb’s ringing is to Fourier transform the image, apply a window, and then inverse Fourier transform. Indeed, this is a substep of the proposed algorithm; however, a non-standard window was used. Common windows used for this include the Fermi window, the Kaiser-Bessel window, the Hamming window, and the Hanning window. This method is presented in “Digital Signal Processing” by Oppenheim.
I would have liked to see how this new technique, which is much more computational costly, compares to this very simple and computationally efficient approach.
Again, thank you for the paper and the new technique.
Thank you for your comments. It has been observed that the global subvoxel-shifts improved the Gibbs ringing, and Kellner et al. further proposed the local subvoxel-shifts for better performance. The comparison of local subvoxel-shifts and conventional filtering methods was shown in Kellner et al. MRM 2016.
In this study we identified the additional ringing pattern due to partial-Fourier acquisition and zero filling interpolation, and proposed a pipeline combined with local subvoxel-shifts since it is the state-of-the-art. The proposed pipeline can be incorporated with any other methods targeting specific ringing patterns. Currently there is no optimal filtering for such data of partial-Fourier acquisition and zero filling interpolation.
The local subvoxel-shifts for fully sampled data has been implemented in mrtrix with multi-threading acceleration with satisfactory computational time. And the proposed pipeline adapted from the same code has similar processing time.