Phase Error Correction in Magnetic Resonance: A Review of Models, Optimization Functions, and Optimizers in Traditional Statistics and Neural Networks

Phase errors in magnetic resonance (MR) techniques, including Nuclear Magnetic Resonance (NMR) spectroscopy and Magnetic Resonance Imaging (MRI), pose significant challenges to data accuracy and interpretation. As MR technologies advance, the demand for more sophisticated phase correction methods continues to grow, enhancing diagnostic precision and analytical outcomes. This review explores the evolution of phase correction models, beginning with simple global phase shifts, progressing through traditional linear statistical models, and culminating in modern machine learning techniques—specifically, neural networks. It also examines a range of optimization functions and optimizers, including both MR data-specific and common statistical approaches, applied in phase error correction. While significant progress has been made, current methods often struggle to achieve full automation due to inherent challenges such as the absence of ground truth in real-world MR data. By analyzing key methods and their limitations, this review identifies opportunities for innovation, proposing ensemble learning and other advanced strategies as potential pathways for overcoming existing barriers and advancing the field.