Sophisticated Harmonic Artifact Reduction for Phase data (SHARP)¹ has been widely used for background-field elimination in quantitative susceptibility mapping (QSM). A recent simulation study² suggested usage of a robust cut-off spatial frequency (in mm^-1) as an adaptation of the original imaging- and processing-parameter-dependent TSVD regularization. In the current study we evaluate optimal settings (radius of the spherical kernel and cut-off frequencies) for this improved SHARP implementation and illustrate a scheme for direct conversion of the common TSVD threshold to the new parameters. We also illustrate effects of incorrect parameter choices in simulations and in-vivo.Numerical model: Detailed digital numerical anatomical brain models² were analyzed. The first model represented brain, skull, torso, and air-tissue interfaces (Fig. 1a-d), whereas the second was generated as a ground-truth reference by immersing it in a medium of constant susceptibility (Fig. 1e). SHARP with varying radius (V-SHARP³) was applied with radii varying between 1 and 15 mm and with regularization thresholds between 0 and 0.05 mm^-1. To analyze the impact of incomplete background removal on the susceptibility maps, an LSQR based spatial domain algorithm⁴ was used. B1-contributions were not simulated because they can be eliminated from multi-echo data prior to QSM processing. The root mean squared error (RMSE) was calculated with respect to the ground-truth phase and susceptibility maps (Fig. 1g), over the whole brain and within a certain distance from the brain’s surface. To understand how the TSVD parameters (for a given radius) translate into the (universal) cut-off frequency parameter, the Fourier coefficients with magnitudes equal to or below a TSVD threshold in a deconvolution kernel corresponding to the given radius were analyzed, and the maximum spatial frequency of these coefficients was selected as a cut-off value. Finally, susceptibility maps were calculated from the background corrected phase images using HEIDI⁸. In-vivo study: Volunteer (male; 29 years, approved by the local ethics committee) data were acquired at 3T with a dual-gradient echo sequence (ToF-SWI⁵) (TE1=3.38ms, TE2=22ms, TR=30ms, FA=20°, FOV 230mm×230mm×106mm, isotropic resolution of 0.6mm). Phase images were reconstructed (Hammond et al.⁶) and phase aliasing was resolved with a 3D best-path algorithm⁷. B1-effect: The initial (B1) phase offset was estimated¹ and V-SHARP was applied to the second echo with and without prior subtraction of this contribution, to understand the effect of B1-phase on the results (e.g. in single-echo data).Figure 2 illustrates that the volume in the Fourier-domain nulled by TSVD strongly depends on the radius of the spherical kernel. It also depends on the image resolution in the spatial domain, when the kernel radius is expressed in voxels (as common in the literature), which is illustrated in Fig. 3. Figure 4 shows that TSVD threshold values correspond to cut-off frequencies between 0 and 0.015 mm^-1 for radii between 2 and 15 mm (increment of 1 mm), allowing the comparison of studies carried out using the original TSVD method with future studies using the universal regularization. Total RMSE values (over the whole brain) of the background-corrected-phase and susceptibility maps are given in color-coded maps in Figure 5a. Figure 1g shows simulation results for QSM images and error maps, calculated with best parameters (R=9 mm, τ=0.0074 mm^-1) for QSM (white-star in Fig. 5a, bottom). The first four columns of Fig. 5b show SHARP and QSM images for best cases. Since ground truth phase and susceptibility distributions are unavailable in-vivo, only the background corrected phase and the susceptibility maps are shown. The bottom row shows difference images of the susceptibility maps. Results confirm the numerical simulations in Fig. 5a, except that the susceptibility distribution for τ=0 substantially deviates from the optimum τ=0.0074 mm^-1 (bottom), due to non-harmonic contributions of the B1-related phase offset. The right-most column shows the results obtained with τ=0 when the B1-phase contribution was subtracted from the input phase image.The TSVD threshold originally defined for SHARP depends on the kernel radius, and, hence, on the image resolution. Here, we derived a scheme that allows direct conversion between the conventional threshold and the more robust spatial-frequency cut-off, which will enable comparisons of studies acquired with either parameter. Hence, we highly recommend using the new scheme for future analysis. We further assessed best and extreme parameters with simulated-brain-models and in-vivo data, and showed that residual background contributions may exist in data not corrected for B1-related phase offsets (Fig.5, τ=0). Thus, care should be taken in such cases. Finally, the choice of a small threshold, while causing incomplete background-field elimination as evident from the field maps, did not significantly affect the susceptibility maps (Fig.5, case τ=0).