Harnessing Magnitude-Only and Complex Measurements for Improved Dynamic MRI Reconstruction with Learned Priors

summary

The gist

The gist MRI reconstruction methods for undersampled k-space data naturally utilize complex-valued measurements, and this work proposes C + Mag, a magnitude-informed physics-driven deep learning

In short

The study investigates using magnitude-only measurements alongside complex data for accelerated dynamic MRI reconstruction. The authors propose C+Mag, a physics-driven deep learning method that incorporates this auxiliary magnitude information. Experiments on undersampled cine and flow MRI show that this approach improves image quality, suppresses artifacts, and better preserves phase information compared to standard methods.

Key concepts

C + Mag Reconstruction: This is a deep learning framework for MRI reconstruction that combines both complex k-space measurements and magnitude-only measurements. It aims to leverage the complementary information from both types of data to reconstruct the full image more accurately, especially when acquiring data quickly.
Auxiliary Magnitude Information: The paper explores using random magnitude measurements as an extra piece of information in MRI reconstruction problems. The core idea is that these simple magnitude measurements can carry enough information to help recover the full complex signal without needing extra scan time.
Quad-S Smoothing: Since the absolute value operation, which is needed for magnitude constraints, is not smooth (non-differentiable), the method uses Quad-S smoothing. This technique approximates the non-smooth absolute value function with a smooth quadratic approximation to allow deep learning optimization algorithms to work effectively.
ADMM Unrolling: The reconstruction problem is solved using an Alternating Direction Method of Multipliers (ADMM) unrolling framework. This strategy breaks down the complex optimization into smaller, manageable steps, allowing a deep learning model to learn the necessary steps for reconstructing the image from undersampled data.

Terminology used across episodes

Reinforcement Learning (RL) — explained in 25 episodes
Retrieval-Augmented Generation (RAG) — explained in 21 episodes
Sample Complexity — explained in 20 episodes
Flow Matching — explained in 19 episodes
Quantum Fisher Information (QFI) — explained in 19 episodes
Federated Learning — explained in 17 episodes

This episode discusses

The paper

Harnessing Magnitude-Only and Complex Measurements for Improved Dynamic MRI Reconstruction with Learned Priors · Read on arXiv

Mahdi Saberi, Yas࠱r Utku Alc࠱alar, Merve Gulle, Chetan Shenoy, Mehmet Akc࠱akaya

University of Minnesota

MRI reconstruction methods for undersampled k-space data naturally utilize complex-valued measurements. Parallel developments in sparse phase retrieval have shown that magnitude-only measurements may provide complementary information for signal recovery. However, their use in MRI reconstruction remains largely unexplored, due to lack of practical settings where informative magnitude measurements can be obtained without additional scan time. In this work, we investigate the use of auxiliary k-space magnitude information for accelerated steady-state dynamic MRI reconstruction, and demonstrate strong consistency of k-space magnitudes across time-frames. Building on this observation, we propose C+ Mag, a magnitude-informed physics-driven deep learning reconstruction method. The proposed method employs an ADMM-based unrolling framework with a novel magnitude-aware data-fidelity formulation, where quadratically smoothed optimization and momentum-based updates are introduced to address the non-differentiability and non-convexity of the magnitude constraints. Experiments on retrospectively undersampled cine MRI and phase-contrast flow MRI datasets, as well as prospectively undersampled real-time cine MRI acquisitions, demonstrate improved artifact suppression, sharper anatomical recovery, and better preservation of phase information compared to conventional PD-DL methods, which is further supported through blinded expert reader evaluations.

DOI: 10.1109/TBME.2026.3743233

Transcript

Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: We're looking at the paper: "Harnessing Magnitude-Only and Complex Measurements for Improved Dynamic MRI Reconstruction with Learned Priors".

Jane: Here's the gist of the paper. The gist MRI reconstruction methods for undersampled k-space data naturally utilize complex-valued measurements, and this work proposes C + Mag, a magnitude-informed physics-driven deep learning reconstruction method that demonstrates strong consistency of k-space magnitudes across time frames The paper investigates the use of auxiliary k-space magnitude information for accelerated steady-state dynamic MRI reconstruction and demonstrates strong consistency of k-space magnitudes across time-frames.

Tom: This motivation stems from the observation that two random magnitude measurements can carry information equivalent to one single random complex-valued linear measurement in sparse recovery problems.

Jane: Prior work has explored simple scenarios of this setting on a limited number of examples with hand-crafted regularizers.

Tom: The availability of large-scale MRI databases and recent findings in adversarial robustness literature motivated the investigation into whether auxiliary magnitude information can be reliably leveraged for MRI reconstruction without requiring additional scan time.

Paper summary: Tom: We're talking about the paper "Harnessing Magnitude-Only and Complex Measurements for Improved Dynamic MRI Reconstruction with Learned Priors." We just covered that they propose C + Mag, which uses complex measurements and magnitude measurements together to reconstruct dynamic MRI data from undersampled k-space data.

Jane: Right, so the thesis is that by leveraging auxiliary k-space magnitude information—which they suggest can be consistent across time frames—they can achieve accelerated steady-state dynamic MRI reconstruction without needing extra scan time.

Lu: The motivation stems from the observation that two random magnitude measurements carry information equivalent to one single random complex-valued linear measurement in sparse recovery problems, which links it back to prior work in sparse phase retrieval.

Meng: The practical problem they’re solving is that there aren't many real-world settings where you can get those useful magnitude measurements for MRI without increasing the scan time.

Lalam: Their key contribution is introducing a PD-DL reconstruction framework that jointly leverages complex-valued and auxiliary magnitude-only measurements for accelerated MRI reconstruction through a unified optimization formulation.

Tom: They developed an ADMM-based unrolled reconstruction algorithm with a novel data-fidelity formulation that includes quadratically smoothed optimization and momentum-based updates for stability when dealing with non-differentiable constraints.

Jane: And they showed strong consistency of k-space magnitudes across time frames, which is what makes this approach so promising for dynamic studies.

Conclusion: Tom: So, to wrap up "Harnessing Magnitude-Only and Complex Measurements for Improved Dynamic MRI Reconstruction with Learned Priors," the authors are introducing a new way to formulate the inverse problem that lets them put auxiliary magnitude information directly into PD-DL reconstruction for dynamic MRI.

Jane: It means they can reconstruct dynamic scans faster, without needing extra acquisition costs, because they're using information from neighboring time frames via those magnitude constraints.

Lu: The implication is that this method can be synergistically combined with different optimization schemes and network architectures, suggesting that further comparisons of different network architectures might not be critical for this work.

Meng: From a production standpoint, it means they’ve created a framework that preserves clinically relevant features and enables accelerated cardiac MRI without compromising image quality.

Lalam: The paper demonstrates substantial improvements over conventional PD-DL reconstruction methods in both image quality and phase preservation, preserving clinically relevant features and enabling accelerated cardiac MRI without compromising clinical image quality.

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