💻 computer science

Phase-map synthesis from magnitude-only MR images using conditional score-based diffusion models with application in training of accelerated MRI reconstruction models

This paper proposes using conditional score-based diffusion models to synthesize realistic phase maps from magnitude-only MR images, enabling the creation of large-scale k-space datasets that significantly improve the training and diagnostic fidelity of deep learning-based accelerated MRI reconstruction models compared to existing alternatives.

Original authors: M. Berk Sahin, Dilek Yalcinkaya, Abolfazl Hashemi, Behzad Sharif

Published 2026-05-05

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CC BY 4.0

Original authors: M. Berk Sahin, Dilek Yalcinkaya, Abolfazl Hashemi, Behzad Sharif

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to teach a robot chef how to cook a perfect meal (reconstruct a clear medical image) using a recipe book. In the world of MRI, the "recipe" is the raw data collected from the machine, known as k-space.

However, there's a big problem: Most hospitals throw away the full recipe book. Due to privacy and storage issues, they only keep the "finished dish" photo (the magnitude-only image). They throw away the secret instructions on how the flavors were mixed (the phase map). Without those secret instructions, the robot chef can't learn to cook well, especially when the machine is running fast (accelerated MRI).

This paper proposes a clever solution: Let's use a "magic imagination machine" to guess the missing secret instructions.

Here is how the authors did it, explained simply:

1. The Problem: The Missing "Secret Sauce"

When doctors take an MRI, the machine captures two things:

The Magnitude: The bright, clear picture of the body part (like a black-and-white photo). This is what is usually saved.
The Phase: A hidden map of how the magnetic signals are shifting. It's invisible to the naked eye but crucial for reconstructing the image, especially when the scan is fast.

Because hospitals only save the "photo" and throw away the "map," researchers have been stuck with very small datasets to train their AI. They can't just pretend the map is smooth or simple; that's like trying to bake a cake by guessing the ingredients, which leads to bad results.

2. The Solution: The "Magic Imagination Machine" (SBDM)

The authors built a new type of AI called a Score-Based Diffusion Model (SBDM). Think of this model as a highly skilled art restorer or a detective.

How it works: You give the AI the "photo" (the magnitude image). The AI then uses its training to "imagine" or "synthesize" the missing "secret map" (the phase map) that would logically belong to that photo.
The Analogy: Imagine you see a photo of a rainy street. A normal computer might guess the puddles are just flat circles. This new AI, however, looks at the reflections, the angle of the rain, and the texture of the pavement, and "dreams up" a highly realistic, complex map of exactly where the water is flowing, even though it never saw the original map.

3. The Experiment: Training the Robot Chef

To see if this "imagined map" was good enough, the authors did the following:

They used their AI to create thousands of fake "secret maps" based on real patient photos.
They combined these fake maps with the real photos to create a massive, fake "recipe book" (a huge k-space dataset).
They fed this new dataset to a standard AI (called VarNet) to teach it how to reconstruct fast MRI scans.

4. The Results: Who Cooked the Best Meal?

They compared their new method against three other ways of guessing the missing map:

The "Naïve" Guess: Just assuming the map is smooth and simple (like assuming all rain puddles are perfect circles).
The "Old Magic" (GAN): Using an older type of AI (Generative Adversarial Network) to guess the map.
The "Real Deal": Using the actual, real secret maps (which they only had for a tiny bit of data to test against).

The Findings:

The Naïve Guess: Worked okay for slow scans, but when the scan was very fast, the reconstructed images became blurry and full of errors.
The Old Magic (GAN): Was better than the naïve guess, but it started making things up. It created "hallucinations"—fake details in the brain or knee that weren't actually there. It was like the chef adding a weird spice that didn't belong.
The New Magic (SBDM): This was the winner. The images reconstructed using their AI's "imagined maps" were almost as good as if they had used the real secret maps. Crucially, it didn't make up fake details. The images were sharp, accurate, and free of those confusing "hallucinations."

The Bottom Line

The paper shows that by using this new "Score-Based Diffusion" model, we can take the millions of MRI photos hospitals already have (which lack the secret phase data) and turn them into a powerful training tool. This allows AI to learn how to create fast, high-quality MRI scans without needing to access the raw, private data that hospitals usually discard.

In short: They taught an AI to dream up the missing parts of an MRI so that other AIs can learn to see clearly, even when the machine is moving fast.

Technical Summary: Phase-map Synthesis from Magnitude-only MR Images using Conditional Score-based Diffusion Models

Problem Statement
The training of deep learning (DL)-based image reconstruction models for accelerated magnetic resonance imaging (MRI) requires large, diverse datasets of raw k-space (Fourier domain) data. However, in most clinical settings, raw k-space data is discarded due to storage constraints and patient privacy concerns; only magnitude-only images (typically in DICOM format) are retained. While applying a forward Fourier transform to magnitude-only images yields "valid" k-space data, the absence of phase information— which is inherently non-zero in MRI—ignores critical features, often leading to subpar reconstruction performance. Existing literature has been limited to small training datasets or a few open-source k-space repositories. Although synthetic data has been shown to improve generalization in DL-based MRI, existing generative approaches like Generative Adversarial Networks (GANs) suffer from training instability and biased results. There is a need for a robust generative method to synthesize realistic phase maps from magnitude-only images to create large-scale training datasets.

Methodology
The authors propose a novel framework utilizing Conditional Score-Based Diffusion Models (SBDMs) to synthesize realistic MRI phase maps from magnitude-only images. The pipeline consists of three main stages:

SBDM Training: A continuous diffusion process is constructed where the goal is to model the posterior distribution of phase maps ( $x$ ) conditioned on magnitude images ( $y$ ). The authors employ a Variance Exploding (VE)-SDE formulation, empirically observing it yields better sample quality than Variance Preserving (VP)-SDE. The model uses a time-dependent score function network ( $s_\theta$ ), based on the ncsnpp architecture (a U-Net variant with BigGAN residual blocks), trained via sliced score matching. The network learns to denoise noisy phase maps concatenated with magnitude images.
Phase-map Synthesis: Once trained, the SBDM generates realistic phase maps corresponding to input magnitude-only images. These synthesized phase maps are combined with the original magnitude images to reconstruct full complex k-space data.
Downstream Evaluation: To assess the quality of the synthesized phase maps, the authors train a VarNet (a DL-based accelerated MRI reconstruction model) using the synthesized k-space data. This VarNet is then tested on real-world k-space data (from the fastMRI dataset) to evaluate reconstruction fidelity.

The proposed method is compared against three baselines:

Naïve/Smooth: Magnitude images combined with phase maps sampled from a Gaussian distribution.
GAN: Phase maps synthesized using a state-of-the-art GAN approach.
Ground Truth (GT): Phase maps derived from actual raw k-space data.

Key Contributions

First Application of SBDMs for MRI Phase Synthesis: To the best of the authors' knowledge, this is the first work exploring the application of score-based diffusion models specifically for synthesizing phase maps from magnitude-only MR images.
Data Augmentation Strategy: The method enables the creation of large, diverse k-space training datasets from widely available magnitude-only image registries, addressing the scarcity of raw k-space data.
Comprehensive Evaluation: The study evaluates the generative model not just on visual similarity (using Fréchet Inception Distance, FID) but critically on its utility in a downstream reconstruction task, measuring both quantitative metrics (SSIM, PSNR, NRMSE) and qualitative fidelity (presence of hallucinated features).

Results

Generative Quality: The SBDM significantly outperformed the GAN approach in terms of FID scores. For the knee dataset, the FID was 5.46 (SBDM) vs. 40.65 (GAN); for the brain dataset, it was 3.46 (SBDM) vs. 32.08 (GAN). Qualitatively, GAN-derived phase maps exhibited erroneous sharp patterns and noise not present in ground truth, whereas SBDM outputs were more realistic.
Reconstruction Performance: VarNet models trained on SBDM-synthesized k-space data achieved performance nearly identical to models trained on ground-truth k-space data across various acceleration factors ( $R \in \{2, 3, 4, 6\}$ ) and auto-calibration region sizes.
Comparison with Baselines:
- The Naïve (Smooth Phase) approach performed comparably to SBDM at low acceleration factors but degraded severely as acceleration increased.
- The GAN-based approach showed comparable quantitative metrics (NRMSE) to SBDM in some cases but failed qualitatively. At higher acceleration factors, GAN-trained models produced "hallucinated" features (erroneous structures) in the reconstructed images, particularly in brain structures, which could adversely impact diagnostic accuracy.

Significance and Claims
The paper claims that the proposed SBDM approach is superior to existing GAN-based methods for synthesizing MRI phase maps. The authors emphasize that while quantitative metrics like NRMSE might be similar between SBDM and GAN approaches, the reconstruction fidelity is the critical differentiator. The SBDM approach avoids the generation of erroneous or hallucinated features that could compromise diagnostic accuracy, a risk observed with GANs.

The authors conclude that having a "realistic" phase map is crucial for efficiently utilizing magnitude-only MR image databases to train highly accelerated reconstruction models. They position their work as a solution to the "dataset shift" problem in clinical DL deployment, enabling the use of vast, anonymized magnitude-only image repositories to train generalizable, high-performance reconstruction models without requiring access to discarded raw k-space data.