Difference optimization: Automatic correction of relative frequency and phase for mean non-edited and edited GABA ¹H...

Phase and frequency corrections of magnetic resonance spectroscopic data are of major importance to obtain reliable and unambiguous metabolite estimates as validated in recent research for single-shot scans with the same spectral fingerprint. However, when using the J-difference editing technique ¹H MEGA-PRESS, misalignment between mean edited (ON‾) and non-edited (OFF‾) spectra that may remain even after correction of the corresponding individual single-shot scans results in subtraction artefacts compromising reliable GABA quantitation. We present a fully automatic routine that iteratively optimizes simultaneously relative frequencies and phases between the mean ON‾ and OFF‾¹H MEGA-PRESS spectra while minimizing the sum of the magnitude of the difference spectrum (L¹ norm). The proposed method was applied to simulated spectra at different SNR levels with deliberately preset frequency and phase errors. Difference optimization proved to be more sensitive to small signal fluctuations, as e.g. arising from subtraction artefacts, and outperformed the alternative spectral registration approach, that, in contrast to our proposed linear approach, uses a nonlinear least squares minimization (L² norm), at all investigated levels of SNR. Moreover, the proposed method was applied to 47 MEGA-PRESS datasets acquired in vivo at 3T. The results of the alignment between the mean OFF‾ and ON‾ spectra were compared by applying (a) no correction, (b) difference optimization or (c) spectral registration. Since the true frequency and phase errors are not known for in vivo data, manually corrected spectra were used as the gold standard reference (d). Automatically corrected data applying both, method (b) or method (c), showed distinct improvements of spectra quality as revealed by the mean Pearson correlation coefficient between corresponding real part mean DIFF‾ spectra of R_bd=0.997±0.003 (method (b) vs. (d)), compared to R_ad=0.764±0.220 (method (a) vs. (d)) with no alignment between OFF‾ and ON‾. Method (c) revealed a slightly lower correlation coefficient of R_cd=0.972±0.028 compared to R_bd, that can be ascribed to small remaining subtraction artefacts in the final DIFF‾ spectrum. In conclusion, difference optimization performs robustly with no restrictions regarding the input data range or user intervention and represents a complementary tool to optimize the final DIFF‾ spectrum following the mandatory frequency and phase corrections of single ON and OFF scans prior to averaging.