磁振頻譜(Magnetic resonance spectroscopy)是一種藉由觀測各種不同代謝物頻譜以分析之方法,在頻譜中各種代謝物(NAA, Creatine, Choline,Glx)都有其自身獨特的位置以及含量，藉由觀測頻譜可以探討病人體內的病灶或是受試者的各項研究上。
在磁振頻譜處理中，後處理(Post-processing)為相當重要的一環，後處理主要將原始得到的訊號經由一系列的處理，譬如訊號結合、濾波、相位校正等，改善得到的頻譜品質，有助於後續之分析及定量處理。在本論文當中會探討的後處理方法，例如頻率飄移、渦流校正、相位校正以及殘水去除，經由一連串處理，克服了頻率飄移導致的線寬變化、渦流及不正確相角造成線型不佳之問題、以及去除水抑制後還殘留下來之水訊號，我們提出統計方法以識別殘水去除是否成功處理，與人工判斷標籤相比有著不錯的準確度，在定量結果方面，處理前後在 CRLB的數值有著顯著的下降，顯示我們提出的後處理流程有助於提升定量的準確性。

Magnetic resonance spectroscopy (MRS) is a method for analyzing various metabolites. In the spectrum, various metabolites (NAA, Creatine, Choline, Glx) have their own unique quantities and resonance of frequency. They can reveal patients' diseases and also be used in various academic studies.
In magnetic resonance spectrum processing, ‘Post-processing’ is an essential part, which can decide the completeness of the final result by adjusting different methods into a procedure like frequency drift correction, eddy current correction, phase correction, and residual water removal. After a series of processing, we overcome the problem of linewidth, caused by frequency drift, and poor line shape, caused by eddy current and incorrect phase. Meanwhile, we also remove residual water signals remaining after water suppression. We use statistical methods to test whether we successfully manage the residual water removal. Compared to ground-truth labels, which is visually judged by two people, It has great accuracy. As for quantification, the CRLB after processing significantly declines. As a result, post-processing help increases the accuracy of quantification.

1. Near, J., et al., Preprocessing, analysis and quantification in single‐voxel magnetic resonance spectroscopy: experts' consensus recommendations. NMR in Biomedicine, 2021. 34(5): p. e4257.
2. Scott, J., et al., A comparison of two post-processing analysis methods to quantify cerebral metabolites measured via proton magnetic resonance spectroscopy in HIV disease. The British journal of radiology, 2016. 89(1060): p. 20150979.
3. Mocioiu, V., et al., From raw data to data-analysis for magnetic resonance spectroscopy–the missing link: jMRUI2XML. BMC bioinformatics, 2015. 16(1): p. 1-11.
4. Wiegers, E.C., et al., Automatic frequency and phase alignment of in vivo Jdifference-edited MR spectra by frequency domain correlation.Magnetic Resonance Materials in Physics, Biology and Medicine, 2017. 30(6): p. 537-544.
5. Near, J., et al., Frequency and phase drift correction of magnetic resonance spectroscopy data by spectral registration in the time domain. Magnetic Resonance in Medicine, 2015. 73(1): p. 44-50.
6. Rowland, B.C., et al., Correcting for frequency drift in clinical brain MR spectroscopy. Journal of Neuroimaging, 2017. 27(1): p. 23-28.
7. Gajdošík, M., et al., INSPECTOR: free software for magnetic resonance spectroscopy data inspection, processing, simulation and analysis. Scientific reports, 2021. 11(1): p. 1-16.
8. Klose, U., In vivo proton spectroscopy in presence of eddy currents. Magnetic resonance in medicine, 1990. 14(1): p. 26-30.
9. McLean, M.A., et al., Characterization and correction of center‐frequency effects in X‐nuclear eddy current compensations on a clinical MR system.Magnetic Resonance in Medicine, 2021. 85(5): p. 2370-2376.
10. Staniszewski, M. and A. Polański, Hankel Singular Value Decomposition as a method of preprocessing the Magnetic Resonance Spectroscopy. arXiv preprint arXiv:2103.15754, 2021.
11. Nagaraja, B.H., et al., Tensor-Based Method for Residual Water Suppression in $^ 1$ H Magnetic Resonance Spectroscopic Imaging. IEEE Transactions on Biomedical Engineering, 2018. 66(2): p. 584-594.
12. Chahid, A., et al., Residual water suppression using the squared eigenfunctions of the Schrödinger operator. IEEE access, 2019. 7: p. 69126-69137.31
13. Cabanes, E., et al., Optimization of residual water signal removal by HLSVD on simulated short echo time proton MR spectra of the human brain. Journal of Magnetic Resonance, 2001. 150(2): p. 116-125.
14. Bhaduri, S., et al., SCSA based MATLAB pre-processing toolbox for 1H MR spectroscopic water suppression and denoising. Informatics in Medicine Unlocked, 2020. 18: p. 100294.