Motion-Aware Neural Networks Improve Rigid Motion Correction of Accelerated Segmented Multislice MRI

Synopsis

We demonstrate a deep learning approach for fast retrospective intraslice rigid motion correction in segmented multislice MRI. A hypernetwork uses auxiliary rigid motion parameter estimates to produce a reconstruction network based on the motion parameters that are specific to the input image. This strategy produces higher quality reconstructions than those produced by model-based techniques or by networks that do not use motion estimates. Further, this approach mitigates sensitivity to misestimation of the motion parameters.

Background

Motion frequently corrupts MRI acquisitions, degrading image quality or necessitating repeated scans¹. Recent advances promise real-time motion estimates, including external tracking², navigators³, and SAMER⁴. We demonstrate a deep learning technique for retrospective intraslice rigid motion correction in 2D fast spin echo (FSE) brain MRI that uses motion estimates to mitigate image artifacts. We employ a hypernetwork⁵ -- a network that outputs weights of another network -- to convert estimated motion parameters into a motion state-specific reconstruction network.

We assume a quasistatic motion model where the object only moves via 2D rotations and translations between shots. We defer modeling through-slice motion for future work.

Methods

Data

We demonstrate our approach on 2D T2 FLAIR FSE brain MRI k-space signals (3T GE Signa Premier, 48-channel head coil, 6-shot acquisition, TR=10s, TE=118ms, TI=2.6s, FOV=260x260mm², acquisition matrix=416x300, slice thickness=5mm, slice spacing=1mm) acquired at Massachusetts General Hospital under an approved IRB protocol. We split the dataset into 553/197/153 training/validation/test 2D slices from 31/11/9 subjects respectively, with no subject overlap between sets. We treat the acquired data as ground truth and simulate motion artifacts during training and testing.

Network Architectures and Training

Our strategy ('ARC-HN') includes two components (Figure 1): (i) a hypernetwork that uses fully-connected layers to generate weights of a reconstruction subnetwork from motion parameter estimates and (ii) the reconstruction subnetwork that performs motion-corrected reconstruction. This architecture enables the reconstruction strategy to vary with the motion parameters and match the corruption process better. The motion parameters comprise 18 scalars representing x- and y- translations and a rotation for each of 6 shots. The input to the reconstruction subnetwork is 88-channel real and imaginary components of the ARC parallel imaging reconstruction⁶ (Orchestra SDK - GE Healthcare) of k-space data from 44 receive coils (4 neck channels were discarded). The final reconstruction subnetwork output is 88-channel k-space data converted to the reconstructed image via the inverse Fourier transform and root-sum-of-squares coil combination.

Fig 1. Proposed architecture.

Our reconstruction network takes as input 44-coil undersampled motion-corrupted k-space data represented as 88 channels with real and imaginary components for each coil and produces motion-free, fully-sampled k-space data in the same format. The weights of this network are the output of a hypernetwork whose inputs are motion parameters describing the motion state. Only the hypernetwork contains trainable weights, which are learned via the SSIM loss function.

We compare our strategy to four methods:

1. ARC, which applies parallel imaging reconstruction without motion correction

2. Model-Based reconstruction that applies phase shifts and rotations to the ARC reconstruction to undo motion⁷ and then applies the non-uniform fast Fourier transform^8,9

3. ARC-Baseline, a deep learning method that takes the ARC reconstruction as input and does not incorporate motion parameters (the same network is applied to all inputs regardless of motion state)

4. RAW-HN, a hypernetwork whose reconstruction subnetwork takes raw k-space data as input instead of the ARC reconstruction.

All reconstruction networks process the input via 6 successive “interleaved” layers that combine convolutions in frequency and image space¹⁰, followed by a single convolution and are designed to contain roughly 2.7 million trainable parameters.

Motion Simulation

Figure 2 illustrates our motion simulation process. We first apply ARC reconstruction to motion-free k-space data, followed by the inverse Fourier transform and root-sum-of-squares coil combination to form the motion-free image $x$. We estimate coil sensitivity profiles $S_i$ using ESPIRiT¹¹ with learned parameter selection¹² and extend these profiles to the edge of the image domain via B-spline interpolation. We synthesize motion-corrupted measurements for coil $i$ as

$$y_i=A_i(m)x+ϵ,$$

where

$$A_i=P_{pre}F{S}_i+P_{post}F{S}_{i}T(m_h,m_v)R(m_{\theta })$$

is the forward model that incorporates sampled rotations ($R$) and translations ($T$) as well as the Fourier transform ($F$), and $ϵ$ is noise drawn from a Rician distribution. We define the motion matrices $R$ and $T$ by selecting a random shot affected by motion and sampling horizontal and vertical translation parameters $m_h$, $m_v$ and rotation parameter $m_{\theta }$ from uniform distributions over the ranges [−10mm,+10mm] and [−45°,45°], respectively. The undersampling operator $P$ mixes k-space lines before ($P_{pre}$) and after ($P_{post}$) motion such that $y_i$ would have been acquired had the subject shifted between two positions during the acquisition.

Fig 2. Motion simulation.

We estimate image $x$ by applying the inverse Fourier transform and root-sum-of-squares coil combination to an ARC reconstruction of acquired motion-free k-space data. We rotate and translate $x$ to generate moved image $T(m_h,m_v)R(m_{\theta })x$, which is multiplied by coil sensitivities $S_i$ and Fourier transformed to simulate k-space for the the moved head position. Lines from the two k-space data sets are combined to form k-space $y$ that simulates motion from one position to another between acquisition of subsequent shots.

We also simulate a realistic test example by mixing acquired k-space measurements $y_{i,1}$ and $y_{i,2}$ from two scans of the same subject in different positions: $y_i=P_{pre}{y}_{i,1}+P_{post}{y}_{i,2}$.

Implementation Details

We normalize each input/output pair by dividing by the maximum intensity in the corrupted image. Every network is trained to reconstruct a normalized version of the image ($x$ or $T(m_h,m_v)R(m_{\theta })x$) corresponding to the central k-space line. All models are trained with the structural similarity index measure (SSIM) loss function using the Adam optimizer (learning rate 1e-3) and batch size 6. We tune hyperparameters on the validation set and use the test set for final evaluation. All networks take 7 days to train and 200 milliseconds for inference on an NVIDIA RTX 8000 GPU.

Results

The proposed hypernetwork produces sharper, more accurate reconstructions than ARC and Model-Based reconstructions (Figure 3). Our method also quantitatively outperforms classical and deep learning baselines and is less sensitive to motion parameter misestimation than Model-Based reconstruction (Figure 4). Though our method is trained on simulated data, it generalizes to realistic motion-corrupted k-space signals (Figure 5). In all tests, ARC-HN shows the best performance.

Fig 3. Example Reconstructions.

Top to bottom: Image reconstructions, zoomed-in image patches, patchwise difference maps, and k-space for a single coil. The example is chosen to be affected by a large rotation in k-space and highlights the weakness of the Model-Based motion correction technique; the large rotation results in large, unfilled gaps in k-space. All deep learning methods fill in these gaps, and our method (ARC-HN) yields the sharpest, most accurate reconstructions.

Fig 4. Reconstruction Accuracy Statistics.

Left: SSIM scores for all methods. ARC-HN (purple) outperforms classical (green) and deep learning (blue) baselines.

Right: Sensitivity to misestimated motion parameters. Noise of increasing standard deviation is added to true motion parameters provided to the reconstruction method. SSIM reduction due to motion misestimation is reported for motion-aware methods. Hypernetworks are less sensitive to noisy parameters than model-based reconstruction.

Fig 5. Results on Realistic Test Example.

Top to bottom: Image reconstructions, image patches, patchwise difference maps, patchwise SSIM plots, and k-space for a single coil on a realistic test example. Approximate, imperfect in-plane motion estimates were obtained via registration and provided to the Model-Based reconstruction and our hypernetwork. Though the ARC-HN reconstruction contains a reduced-intensity artifact, motion artifacts are significantly improved.

Conclusions

We demonstrate a deep learning approach for correcting rigid motion artifacts in 2D FSE T2 FLAIR MRI. Our approach incorporates motion parameter estimates and improves on classical strategies, while offering robustness to misestimated motion parameters. Using ARC reconstruction instead of undersampled k-space data as input improves network performance by allowing it to focus solely on the motion artifact correction task.