MotionTTT: 2D Test-Time-Training Motion Estimation for 3D Motion Corrected MRI

TL;DR

MotionTTT tackles motion artifacts in 3D MRI by combining a 2D motion-free reconstruction network with test-time-training to estimate 3D rigid motion from motion-corrupted data. It operates by first pre-training a motion-free 2D network, then freezing its weights while optimizing motion parameters using a data-consistency loss, and finally reconstructing a motion-corrected 3D volume with a DC or L1-minimization step. The approach is theoretically justified for a simplified model, and experimentally demonstrates accurate motion parameter recovery across inter-shot and intra-shot scenarios, outperforming classical baselines in speed and robustness and showing clear improvements on real motion data. These results indicate practical potential for fast, hardware-free motion correction in MRI, enabling higher image quality and clinical throughput in the presence of patient motion.

Abstract

A major challenge of the long measurement times in magnetic resonance imaging (MRI), an important medical imaging technology, is that patients may move during data acquisition. This leads to severe motion artifacts in the reconstructed images and volumes. In this paper, we propose a deep learning-based test-time-training method for accurate motion estimation. The key idea is that a neural network trained for motion-free reconstruction has a small loss if there is no motion, thus optimizing over motion parameters passed through the reconstruction network enables accurate estimation of motion. The estimated motion parameters enable to correct for the motion and to reconstruct accurate motion-corrected images. Our method uses 2D reconstruction networks to estimate rigid motion in 3D, and constitutes the first deep learning based method for 3D rigid motion estimation towards 3D-motion-corrected MRI. We show that our method can provably reconstruct motion parameters for a simple signal and neural network model. We demonstrate the effectiveness of our method for both retrospectively simulated motion and prospectively collected real motion-corrupted data.

Figures (13)

• Figure 1: Panel a): magnitude of a 3D volume; panel b): the corresponding 3D k-space data. Panels c)/d)/e) show examples of undersampling masks used for the simulated and real data. The color coding illustrates an interleaved c) and a random d)/e) sampling trajectory indicating which lines along the readout dimension $k_z$ are sampled within the same out of 50 shots.
• Figure 2: Illustration of the MRI forward models and zero-filled (ZF) reconstructions without (left) and with (right) motion for the 2D single-coil setup. Rotations are implemented with the NUFFT $\mathbf N(\mathcal{T},{\bm \phi})$ and adjoint NUFFT $\mathbf N_{\text{adj}}(\mathcal{T},-{\bm \phi})$, and translations with linear phase shifts $\mathbf L(\mathcal{T}, \mathbf t)$. During acquisition under rotations areas of the k-space are sampled multiple times while others are not sampled at all, resulting in additional undersampling artifacts in the corrected ZF image compared to the motion-free ZF image.
• Figure 3: For an example with $n=2k$, $k=1400$, $d=100$, and $b=4$ and $\mathbf m^\ast = 0$ we plot the loss as a function of $m_1$, where $a$ is the number of values for $m_2,m_3,m_4$ that are set to an integer that is non-equal to $m_2^\ast,m_3^\ast, m_4^\ast$, respectively. It can be seen that there is a sharp minima around $\mathbf m = \mathbf m^\ast$. This minima turns out to be unique under certain conditions. In our theory we consider discrete shifts, indicated by crosses.
• Figure 4: Reconstruction performance in PSNR as a function of the level of simulated inter-shot motion severity defined by (number of motion events, maximum rotation/translation in degrees/mm). We consider L1-minimization or U-net based reconstruction combined with either known motion, no motion-correction or motion estimated with MotionTTT or alternating optimization. Error bars are the standard deviation over test examples and randomly sampled motion trajectories.
• Figure 5: Reconstructions and difference images for simulated motion of severity level 9 for all methods in Figure \ref{['fig:recons_psnr']}.

Theorems & Definitions (1)

• Theorem 1