In the second part of this topic, we focus on more advanced image processing methods. We will give an overview of image denoising methods, Gibbs ringing removal, outlier detection, frequency stabilization, effects of gradient nonlinearity, and discuss challenges of pushing for higher spatial resolution.
Due to the signal-attenuation induced by diffusion-sensitization and T2 - relaxation resulting from the long echo time necessary to accommodate gradient pulses, the signal-to-noise ratio of the DW signals is inherently low. Thermal noise that corrupts DWI measurements propagates to the diffusion parameters of interest and, as such, hampers visual inspection and precise quantitative interpretation of the underlying diffusion process. Although attempts have been made to minimize the noise propagation by optimizing diffusion encoding settings1,2, scan time limitations put a bar on what is to gain with protocol optimization in terms of precision. Therefore, image denoising, i.e. minimizing the variance of the DW signals in a post-processing step, is essential to raise that bar e.g. 4-6.
Many denoising strategies are based on weighted averages of voxels, where the voxels (and weights) are selected by metric similarity of patches e.g. 5. Loss of spatial resolution of the image (blur) and introduction of additional partial volume effects might remove fine anatomical details and might complicate further quantitative analyses or bias the diffusion modeling. Alternatively, several approaches have adopted the idea of noise removal by means of transforming a redundant dataset into a principal component basis and preserving only the signal-carrying principal components4,6.
Spurious ringing near sharp edges, e.g., boundaries of tissues, appears in the reconstructed images any time the Fourier space is truncated during acquisition or compression7. MR images that are obtained via the inverse Fourier transformation (FT) of a finite k-space acquisition represent a classic case of this phenomenon, referred to as Gibbs ringing. Although ringing is a feature of all MRIs obtained via inverse Fourier transform, it becomes increasingly significant for low resolution and/or quantitative modalities such as DWI8-10. While introducing a bias of at most 9% of the intensity step in the individual “weighted” images, the Gibbs effect is amplified tremendously in the derived parametric maps, e.g., of diffusion and kurtosis tensor components, often affecting major white matter bundles such as the Corpus Callosum.
The most common strategy to suppress the Gibbs artifact has been spatial smoothing of the MR data, Alternatively, one can apply a regularized extrapolation of the k‐space beyond its measured part to avoid the sharp cut‐off. Total variation (TV) regularization has been suggested to stabilize this ill‐posed estimation problem8,9. Recently, a more targeted approach has been introduced. Gibbs ringing can be minimized by reinterpolating the image using optimized subvoxel shifts to minimize the oscillations around sharp edges10.
As explained in the first lecture, single-shot Echo Planar Imaging is most frequently used due to dMRI’s extreme sensitivity to motion. Covering k-space in one single-shot minimizes motion effects, but it does limit the achievable spatial resolution: as transverse relaxation is occurring throughout the readout window, blurring is introduced in the image reducing its effective spatial resolution while progressively decreasing the available signal. An alternative approach is to cover k-space over multiple-shots and to deal with inconsistencies introduced in the data as a result of different types of motion occurring during the corresponding diffusion preparation modules20.
Early strategies involved the acquisition of a navigator which would sample the same central region of k-space for each shot21. This region corresponded to a low-resolution but full field-of-view image which would enable to measure and correct for the motion-induced and typically smoothly varying spatial phase patterns. Recently, an alternative approach has been introduced to estimate this information which does not require the acquisition of navigators22. Provided the number of coil channels is sufficiently higher than the number of k-space shots, it is possible to reconstruct a non-aliased image (albeit with low signal-to-noise ratio) from each data segment using parallel imaging. A full reconstruction can then be performed, incorporating the estimated phase information. Extensions to this method have since been proposed, allowing for 3D motion-correction and reconstruction23. Recently, reconstruction methods based on low-rank regularization have also been introduced24.
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