Synthetic phase image modulated by two-dimensional sinusoidal profile based on magnitude image using for magnetic...

Magnetic resonance imaging (MRI) is a complex-valued technique incorporating magnitude and phase information, with phase images critical for susceptibility-weighted imaging and quantitative susceptibility mapping yet often absent in reconstruction. This study aimed to synthesize phase images from magnitude-only data via innovative phase modulation to reconstruct complete MR images.

Synthetic phase information was generated using irregular phase modulation based on two-dimensional sinusoidal functions. Comprehensive assessments were performed to validate the synthetic phase performance. First, SVG (Synthetic Variable Gradient) and PSE (Phase-Shift Estimation) experiments were performed to evaluate the spatial heterogeneity of the synthesized phase structures. Second, five metrics, including signal-to-noise ratio (SNR), contrast, correlation, homogeneity, energy, evaluated synthetic phase image similarity to true phase image, the Wilcoxon rank-sum test and Bland-Altman analyses further validated the consistency and approximation between synthetic and true phase images. Final, compressed sensing (CS) and Dense-U-Dense Net (DUD-Net) were utilized to verify the feasibility of synthetic phase images for MRI reconstruction, with peak signal-to-noise ratio (PSNR), root mean square error (RMSE) and structural similarity index (SSIM) used for comparative evaluation.

The SVG and PSE results confirmed that the irregular phase provides more effective spatial heterogeneity than regular modulation. Statistical analyses demonstrated that the irregular phase achieved higher consistency with true phase images across five metrics including SNR, contrast, correlation, homogeneity, energy, with the Wilcoxon rank sum test (P < 0.05) and Bland Altman analyses further confirming its significant approximation to real physical phase. Regarding MRI reconstruction, the proposed irregular method demonstrated superior fidelity compared to regular methods. Quantitative validation showed that the irregular method achieved a DUD-Net PSNR of 34.90 ± 5.50 for magnitude reconstruction, which significantly outperformed the regular method and demonstrated comparable performance to the magnitude only reconstruction baseline. While irregular phase metrics were lower in high noise background areas, these have a competitive performance with the true phase when background noise was removed.

Both CS and DUD-Net effectively reconstructed phase information, and phase modulation can provide reference phase data for establishing MR image reconstruction models without direct phase information. Notably, this heuristic synthetic phase serves as an approximation for reconstruction studies and cannot substitute true phase data for advanced physics-driven applications such as quantitative susceptibility mapping or susceptibility-weighted imaging.