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Gibbs-Ringing Artifact Removal Based on Local Subvoxel-shifts
Elias Kellner, Bibek Dhital, Marco Reisert
TL;DR
Gibbs ringing arises when truncated k-space produces sinc-induced oscillations near sharp image transitions. The paper removes it by locally shifting and re-interpolating images so the sinc pattern is sampled near zero-crossings, then combines directional corrections in Fourier space. The method effectively removes ringing with minimal smoothing and is reported as robust to its kernel-width parameter, although related advanced methods can be difficult to handle because of edge-detection and parameter dependencies.
Problem
Truncated k-space causes sinc-convolution ringing near sharp transitions, while filtering reduces spatial resolution and more advanced corrections can be complex or unstable.
Method
The method uses local subvoxel shifts to sample the sinc ringing pattern near zero-crossings, then combines separate directional corrections in Fourier space.
Results
The method effectively removes ringing in numerical phantoms and MRI images while introducing minimal smoothing or filtering.
Takeaways & Limitations
Its low computational cost, simple framework, and parameter stability support consideration for clinical image-processing pipelines.
Abstract
from arXiv · showhide
Gibbs-ringing is a well known artifact which manifests itself as spurious oscillations in the vicinity of sharp image transients, e.g. at tissue boundaries. The origin can be seen in the truncation of k-space during MRI data-acquisition. Consequently, correction techniques like Gegenbauer reconstruction or extrapolation methods aim at recovering these missing data. Here, we present a simple and robust method which exploits a different view on the Gibbs-phenomena. The truncation in k-space can be interpreted as a convolution with a sinc-function in image space. Hence, the severity of the artifacts depends on how the sinc-function is sampled. We propose to re-interpolate the image based on local, subvoxel shifts to sample the ringing pattern at the zero-crossings of the oscillating sinc-function. With this, the artifact can effectively and robustly be removed with a minimal amount of smoothing.
Introduction
MRI reconstructs images from finitely sampled k-space coefficients, and truncation produces sinc-convolution ringing near sharp edges. The proposed view links artifact strength to how this sinc pattern is sampled on the discrete image grid.
- Introduction: Finite k-space acquisition introduces ringing because truncation convolves the image with a sinc function whose side lobes oscillate near sharp transitions.Sharp edges require high-frequency components that are absent after truncation.
- Introduction: Existing filters reduce oscillations but globally blur images, while Gegenbauer-based methods can require edge detection and parameter choices that may cause instability.These trade-offs motivate a simpler correction strategy.
- Introduction: Ringing amplitude depends on sampling: sinc extrema maximize oscillations, whereas zero-crossings can make them disappear.The discrete sampling location of an edge relative to the grid determines which part of the sinc pattern is sampled.
- Introduction: The method therefore seeks local subvoxel shifts near edges, because multiple edges generally require different optimal shifts rather than one global displacement.The correction is performed locally and non-iteratively.
Methods
The method generates locally shifted images, selects shifts that minimize neighborhood oscillations, and interpolates back to the original grid. Two-dimensional corrections are combined in Fourier space with directional weighting to limit smoothing.
- One-dimensional Case: A set of 2M subvoxel-shifted images is generated by multiplying Fourier coefficients by phase ramps.The shifts are indexed by s = −M … M−1.
- One-dimensional Case: For each pixel, the optimal shift minimizes total variation measured from absolute differences in a neighborhood around the pixel.The ringing is measured separately on the two sides so the edge itself does not dominate the criterion.
- One-dimensional Case: The central pixel is excluded from the oscillation window to improve stability at edges and reduce added noise correlation.The window K is the method’s only parameter, and the reported results indicate robustness to its choice.
- One-dimensional Case: After selecting the shift, the shifted image is evaluated back at the original grid using non-sinc interpolation, implemented here as linear interpolation.This avoids reintroducing ringing through sinc interpolation.
- Two-dimensional Case: In two dimensions, x- and y-direction corrections are performed separately and combined in Fourier space because diagonal edges produce checkerboard-like ringing.The final image combines Jx and Jy using weighting functions Gx and Gy.
- Two-dimensional Case: The weighting functions enhance high frequencies along the corrected direction and suppress them along the other direction.Their normalization leaves artifact-free images unchanged when the directional corrections agree, introducing minimal smoothing.
- Experiments: The evaluation compares the proposed method with Lanczos sigma and median filters on numerical phantoms and MRI measurements.The experiments include polygonal and brain phantoms, DWI data, and a T2-weighted image.
Results
Across numerical phantoms and MRI-derived images, the proposed method removed Gibbs ringing while preserving fine details and introducing minimal smoothing. It was also relatively robust to the kernel-parameter choice.
- Numerical Phantoms: The proposed method effectively removed artifacts with minimal edge smoothing in numerical phantom experiments.The study compared it with median filtering, Lanczos approximation at p = 1, and Lanczos parameters matched for equal noise correlation.
- MRI-derived Phantom: The method preserved fine image details while removing artifacts in the phantom constructed from a T1-weighted image.The findings were reported as basically the same as for the first phantom.
- MRI Images: In DWI and T2-weighted MRI images, the proposed method virtually completely removed ringing with minimal filtering.Median and Lanczos filtering reduced artifacts but caused strong smoothing; the T2-weighted findings were basically the same as for DWI.
Discussion
The discussion contrasts the proposed method with filtering and more complex reconstruction approaches, emphasizing reduced smoothing, parameter robustness, and practical simplicity. Its kernel width is reported as image-size independent, with K = [1, 3] identified as a good compromise.
- Discussion: Standard filtering reduces effective image resolution, while advanced reconstruction and extrapolation methods can be difficult to handle because of complexity and edge-detection requirements.Potential instabilities may also arise from dependence on parameter choices.
- Discussion: In phantom images, the proposed method preserved edges and fine details better than alternatives at comparable smoothing.The Figure 4 comparison reports stronger residual artifacts for Lanczos approximation at equal noise correlation and point-like artifacts from the median filter.
- Discussion: Total-variation methods treat noise and artifact equally, whereas the proposed method explicitly aims to separate the two contributions.The outcome of total variation depends strongly on filter strength and application-specific adaptation.
- Discussion: The proposed method is robust to kernel-width choice, and its parameter is independent of image size.The ringing pattern occurs at a distance of one voxel and therefore scales with matrix size.
- Discussion: K = [1, 3] is reported as a good compromise between artifact removal and smoothing and can be used universally across images.The paper states that the method can be applied with a universal value for K.
Conclusions
The paper presents a non-iterative Gibbs-ringing removal method based on sinc zero-crossing resampling. It reports effective artifact removal with minimal smoothing, low computational cost, and stable behavior across parameter choices, while suggesting possible clinical-pipeline use.
- Conclusions: The method removes ringing by re-sampling the image so the sinc-function is sampled at its zero crossings.This is the paper’s central non-iterative correction strategy.
- Conclusions: The proposed method effectively removes artifacts while introducing minimal smoothing.This conclusion is stated as the principal outcome of the work.
- Conclusions: The method has low computational cost and remains stable across choices of its few parameters.The paper describes its mathematical framework as simple and robust to parameter selection.