PhaseGen

PhaseGen is a complex-valued diffusion model that synthesizes MRI phase data from ordinary magnitude images. It was developed at the Institute for AI in Medicine (IKIM) at University Hospital Essen, with collaborators at TU Dortmund University and the German Cancer Research Center, and released as a preprint in April 2025.

MRI is acquired in k-space, the frequency domain, where the raw signal is complex-valued and carries both magnitude and phase. Clinical pipelines reconstruct the magnitude image and discard the phase, even though phase information improves the detection of thrombosis, microbleeds, and calcification, and supports segmentation performed directly in k-space. The consequence is a severe data asymmetry: surveys count roughly 1.68 million subjects across public magnitude MRI datasets, against on the order of 9,300 in the handful of public k-space collections, which are curated for reconstruction rather than diagnostic labels.

PhaseGen addresses that asymmetry by generating the missing half of the signal. Conditioned on a magnitude image, it samples a plausible corresponding phase, which can be Fourier-transformed into synthetic complex-valued raw data. A single trained generator is reused unchanged across downstream tasks, converting any existing magnitude dataset — including ones with segmentation labels no k-space dataset provides — into pretraining material for models that consume raw data.

#Key Features

• Fully complex-valued diffusion: Rather than splitting real and imaginary parts into separate channels, the forward and reverse processes operate directly on complex numbers, using a noise distribution of unit magnitude with phase drawn uniformly from −π to π, so noise perturbs phase while leaving magnitude intact.
• Magnitude-conditioned generation: The input magnitude image is supplied in a second channel that is held constant at every sampling step, so the generated phase is anatomically consistent with the image it accompanies and the magnitude is never altered.
• Task-agnostic reuse: The same generator supports two unrelated downstream applications — skull-stripping performed directly in k-space and accelerated MRI reconstruction — with no retraining of the diffusion model between them.
• Substantial downstream gains: A k-space skull-stripping model trained on PhaseGen-synthesized data reaches 80.1% Dice on real clinical raw data, where models trained without phase or with naively simulated phase reach 40.1% and 41.1% and fail to generalize at all.
• Real-data efficiency: For reconstruction, mixing synthetic phase with just 15–20% of the available original-phase data matches a model trained on the full real dataset.

#Technical Details

The generator is a complex-valued residual U-Net adapted from the k-Strip architecture, totaling 30.4 million parameters, with a cosine noise scheduler over 1,000 timesteps. Training ran for 200 epochs with the Adam optimizer at an initial learning rate of 1×10⁻⁴, batch size 128, and 20% encoder dropout, completing in about 10 hours on a single NVIDIA A100 80GB. The training corpus is an institutional raw dataset from University Hospital Essen: 12,071 2D k-space scans from 390 patients across Siemens 1.5T and 3T scanners, spanning T1 and T2 sequences at 256×256 resolution. For skull-stripping, 21,822 magnitude brain images from 150 patients were converted to synthetic raw data for training and evaluated on 14 real raw-data volumes, reaching 80.1% Dice and a Hausdorff distance of 1.534 pixels. For reconstruction, the public FastMRI single-coil knee dataset was used: at fourfold undersampling, a 3.3M-parameter network trained purely on PhaseGen data reached 63.16% SSIM and 23.95 dB PSNR, ahead of naive phase simulation (56.31% / 21.81 dB) but behind training on original phase (71.28% / 27.98 dB). Inference costs roughly 10 seconds per slice on a GPU.

#Applications

PhaseGen is aimed at MRI researchers building models that operate on raw data rather than reconstructed images — k-space segmentation, classification, and reconstruction — who are otherwise blocked by the scarcity of labeled complex-valued datasets. The intended workflow is to synthesize phase for a large public magnitude dataset, pretrain on the resulting complex-valued data, then fine-tune on whatever real raw data is available. The reconstruction experiments quantify the payoff directly: comparable accuracy from a fifth of the real raw data.

#Impact

The work is the first to generate artificial complex-valued k-space data, and it contributes to the literature on complex-valued neural networks with a diffusion process that operates natively on complex inputs and noise. Its scope is bounded in ways the authors state plainly: the generator is trained on single-coil data while most clinical acquisition is multi-coil, generation speed makes large-scale synthesis slow, and the absence of comparable public raw datasets left the skull-stripping result unbenchmarked against a model trained on real raw data. The code is public, but the repository states that weights are supplied on request pending upload, and it carries a custom license — Apache 2.0 modified by a Commons Clause — that prohibits selling or commercially exploiting the code without the authors' written permission. The paper is a preprint and has not yet been peer reviewed.