CoRRECT: A Deep Unfolding Framework for Motion-Corrected Quantitative R2* Mapping

TL;DR

CoRRECT tackles motion, noise, and magnetic-field inhomogeneity in qMRI by unifying MRI reconstruction and $R_2^*$ estimation within a deep unfolding framework. It integrates an end-to-end reconstruction module with a biophysical $R_2^*$ estimator, trained in a self-supervised, motion-aware manner that does not require ground-truth $R_2^*$ maps. The approach demonstrates superior performance on simulated and experimental mGRE data across various acceleration rates, outperforming traditional and DL baselines in both reconstruction quality and quantitative map accuracy. This unified pipeline reduces processing complexity and enables robust, high-quality qMRI in accelerated acquisitions, offering practical impact for clinical and research imaging.

Abstract

Quantitative MRI (qMRI) refers to a class of MRI methods for quantifying the spatial distribution of biological tissue parameters. Traditional qMRI methods usually deal separately with artifacts arising from accelerated data acquisition, involuntary physical motion, and magnetic-field inhomogeneities, leading to suboptimal end-to-end performance. This paper presents CoRRECT, a unified deep unfolding (DU) framework for qMRI consisting of a model-based end-to-end neural network, a method for motion-artifact reduction, and a self-supervised learning scheme. The network is trained to produce R2* maps whose k-space data matches the real data by also accounting for motion and field inhomogeneities. When deployed, CoRRECT only uses the k-space data without any pre-computed parameters for motion or inhomogeneity correction. Our results on experimentally collected multi-Gradient-Recalled Echo (mGRE) MRI data show that CoRRECT recovers motion and inhomogeneity artifact-free R2* maps in highly accelerated acquisition settings. This work opens the door to DU methods that can integrate physical measurement models, biophysical signal models, and learned prior models for high-quality qMRI.

Figures (7)

• Figure 1: The overview of the CoRRECT framework for training an end-to-end deep network consisting of two modules: ${\mathsf{R}}_{\bm{\theta }}$ for reconstructing mGRE MRI images and ${\mathsf{E}}_{\bm{\varphi}}$ for estimating corresponding $R_2^\ast$ maps. The network takes as input subsampled, noisy, and motion-corrupted k-space measurements. ${\mathsf{R}}_{\bm{\theta }}$ is implemented as a deep model-based architecture (DMBA) initialized using the zero-filled reconstruction. ${\mathsf{E}}_{\bm{\varphi}}$ is implemented as a customized U-Net architecture mapping the output of ${\mathsf{R}}_{\bm{\theta }}$ to the desired $R_2^\ast$ map.The whole network is trained end-to-end using fully-sampled mGRE sequence data without any ground-truth quantitative $R_2^\ast$ maps.
• Figure 2: The statistical box plot of SNR values for different methods obtained on simulated data at different sampling rates. Results highlight the performance of CoRRECT in both mGRE reconstruction and $R_2^\ast$ estimation against different approaches.
• Figure 3: Quantitative and visual evaluation of CoRRECT on simulated data corrupted with synthetic motion, sampled using acceleration factor $\times 4$. The bottom-left corner of each image provides the SNR and SSIM values with respect to the ground-truth. Arrows in the zoomed-in plots highlight brain regions that are well reconstructed using CoRRECT. The $R_2^\ast$ corresponding to TV, RED, and DU are obtained by the recent LEARN-BIO network Xu.etal2022. Note the excellent quantitative performance of CoRRECT for mGRE reconstruction and $R_2^\ast$ estimation.
• Figure 4: Visual evaluation of CoRRECT on experimentally collected data corrupted with real motion, sampled using acceleration factor $\times 4$. The mGRE image in the first column (denoted with $\times 1$) uses motion-corrupted but fully-sampled k-space data, while the ones in other columns use motion-corrupted and subsampled k-space data. Note the excellent performance of CoRRECT for producing high-quality mGRE and $R_2^\ast$ images. Note also the abilty of CoRRECT trained on synthetic motion to address artifacts due to real object motion.
• Figure 5: Visual evaluation of CoRRECT on experimentally-collected data corrupted with real motion, subsampled using acceleration rates $\{\times 2, \times 4, \times 8 \}$. Arrows in the zoomed-in plots highlight brain regions that are well reconstructed using CoRRECT. Corrupted ($\times 1$) uses motion-corrupted but fully-sampled measurements, while ZF+NLLS, TV, RED, DU and CoRRECT use motion-corrupted and subsampled measurements. Note the improvements due to CoRRECT across different sampling rates.