Data Consistent Deep Rigid MRI Motion Correction

Abstract

Motion artifacts are a pervasive problem in MRI, leading to misdiagnosis or mischaracterization in population-level imaging studies. Current retrospective rigid intra-slice motion correction techniques jointly optimize estimates of the image and the motion parameters. In this paper, we use a deep network to reduce the joint image-motion parameter search to a search over rigid motion parameters alone. Our network produces a reconstruction as a function of two inputs: corrupted k-space data and motion parameters. We train the network using simulated, motion-corrupted k-space data generated with known motion parameters. At test-time, we estimate unknown motion parameters by minimizing a data consistency loss between the motion parameters, the network-based image reconstruction given those parameters, and the acquired measurements. Intra-slice motion correction experiments on simulated and realistic 2D fast spin echo brain MRI achieve high reconstruction fidelity while providing the benefits of explicit data consistency optimization. Our code is publicly available at https://www.github.com/nalinimsingh/neuroMoCo.

Fig. 5:

Motion simulation schematic. We apply ARC reconstruction (Brau et al., 2008) to motion-free data followed by the inverse Fourier transform and root-sum-of-squares coil combination, yielding the initial motion-free image $x$. We also estimate coil sensitivity profiles $S_i$ from the acquired data using ESPIRiT (Uecker et al., 2014) with learned parameter estimation (Iyer et al., 2020) and extend the profiles to the image edge via B-spline interpolation. Next, we simulate an image under a sampled random motion $M\left(m\right)$ by applying rotations and translations to the image and use the sensitivity maps and a Fourier transform to simulate k-space data corresponding to the moved position. Based on the shot pattern for the acquisition, we combine k-space data from the appropriate lines corresponding to the position pre- (blue) and post-motion (red) to form simulated, motion-corrupted k-space measurements $y$. This simulates the k-space data that would have been acquired had the subject moved from the blue position to the red position over the course of the acquisition. The input to our networks is the ARC reconstruction of this simulated $y$. In practice, we sample two versions of $M\left(m\right)x$ and treat one of the two as $x$, to avoid discrepancies between simulated and acquired data when mixing the k-space.

Fig. 6:

Reconstruction quality of all methods as measured by mean square error (MSE) and peak signal-to-noise ratio (PSNR). As with SSIM (Fig. 3a), our method outperforms motion-naive baselines and performs comparably to motion-aware ones according to these metrics.

Fig. 1:

Information flow through our network. During a forward pass, true or estimated motion parameters $m$ serve as input to hypernetwork $h\left(\cdot ;{\theta }_h\right)$ which generates the weights ${\theta }_g$ of a reconstruction subnetwork $g\left(\cdot ;{\theta }_g\right)$. Reconstruction subnetwork $g\left(\cdot ;{\theta }_g\right)$ takes corrupted k-space data as input and produces a reconstruction. The hypernetwork weights ${\theta }_h$ are the only network parameters directly updated during training. At test-time, we freeze ${\theta }_h$ and use the data consistency loss to optimize the motion parameters $m$.

Fig. 2:

Simulated test example. HN outperforms motion-naive baselines (ARC and Conv) and performs similarly to motion-aware methods (Model-Based-GT and HN-GT) without access to any motion parameters. Yellow arrows highlight local reconstruction errors.

Fig. 3:

Simulation results. (a) Reconstruction SSIM across methods. (b) SSIM improvement over motion-naive methods. We improve on the baselines for bars right of the dashed line. (c) Motion estimate errors from our method in the four high-energy and two low-energy shots. Our method outperforms motion-naive methods and is on par with motion-aware ones. Our automated rejection strategy effectively identifies optimization failures.

Fig. 4:

Realistic test example. For this example, we do not have access to the true motion parameters, and our method (HN) outperforms the baselines which do not require this information. HN removes the artifact in ARC and is sharper than Conv (see arrows). Despite being trained on simulated data, our method generalizes to this test example based on acquired k-space data and produces a high-quality reconstruction.