Mathematical and Statistical Review of NMR Frequency Domain Data Pre-processing

Magnetic Resonance Imaging (MRI) is widely used in clinics and research due to its accurate disease identification and non-invasive nature. MRI is based on Nuclear Magnetic Resonance (NMR), which is also extensively employed in various fields. NMR and its modern versions involve intricate pre-processing steps before data analysis. These steps are initially processed in the time domain and subsequently in the frequency domain. While our previous review focused on time domain pre-processing (https://www.preprints.org/manuscript/202310.2032/v1), this review delves into the mathematical and statistical aspects of frequency domain pre-processing. We discuss essential pre-processing steps like phase error correction, baseline correction, solvent filtering, calibration and alignment, reference deconvolution, binning/bucketing and peak picking, peak fitting/deconvolution and compound identification, integration and quantification, normalization and transformation. Furthermore, we offer practical recommendations for each step.