Synopsis

Retrospective motion correction techniques have the potential to improve clinical imaging without altering the workflow or acquisition sequence. Yet, they suffer from long reconstruction times and poor conditioning. To address these problems, we developed a Network Accelerated Motion Estimation and Reduction method (NAMER) within a data-consistency based forward model approach to motion parameter estimation. The neural net accelerates convergence up to 15-fold as well as improving final image quality. The ML+MR physics motion correction method combines the speedup provided by fast convolutional neural networks with the robustness of a forward model-based data-consistency reconstruction.

Introduction

Patient motion is one of the most common and costly types of MRI artifacts¹. A large variety of MRI motion correction techniques exists², but many methods have failed to gain traction in the clinic due to workflow complications (tracking devices) or acquisition disruptions (navigators). Fully retrospective motion correction methods that use only raw k-space data avoid these pitfalls^3–5. However, they present a poorly conditioned, large, nonconvex model inversion problem which must be solved in a clinically acceptable timeframe.

We address these issues by incorporating a convolutional neural network (CNN) step into a SENSE+motion model-based reconstruction. First, the CNN provides an initial guess of the motion artifacts, thereby improving the conditioning of the nonconvex motion search and accelerating convergence. Secondly, the method uses the CNN within the iterative forward model solve to remove motion artifacts from the current iterate image. This approach is similar to those of variational networks, which use a machine learning step to regularize a highly undersampled reconstruction problem⁶.

Methods

Figure 1 outlines the NAMER (Network Accelerated Motion Estimation and Reduction) method. Motion corrupted k-space data is first reconstructed assuming no motion has occurred using the standard SENSE forward model reconstruction⁷. Motion correction is then performed by iterating through the following three steps:

1. CNN image update: Figure 2 shows the motion artifact detecting CNN architecture⁸. Motion corrupted image patches (size 51x51) are passed into the CNN and the artifacts within the patches are detected. Two channel input data was used to hold the real and imaginary components. The network consists of convolutional, batch normalization, and ReLU activation layers (27 total), with 3x3 kernels. Training was performed using simulated motion corrupted images based on a motion forward model^9,10. The artifacts detected by the CNN are subtracted from the original input image (i.e. $$$\boldsymbol{x}_{cnn}=\boldsymbol{x}-\mathrm{CNN}(\boldsymbol{x})$$$).

2. Physics-based motion update: Next, we minimize the data consistency error between the acquired k-space data, $$$\boldsymbol{s}$$$, and $$$\boldsymbol{E}_\boldsymbol{\theta}\boldsymbol{x}_{cnn}$$$ (the encoding model for a given motion trajectory, $$$\boldsymbol{\theta}$$$, applied to the CNN generated image, $$$\boldsymbol{x}_{cnn}$$$), across all of the motion parameters:

$$[\hat{\boldsymbol{\theta}}] = \underset{\boldsymbol{\theta}}{\mathrm{argmin}} ||\boldsymbol{s}-\boldsymbol{E}_{\boldsymbol{\theta}}\boldsymbol{x}_{cnn}||_2$$

3. Physics-based image update: Using the motion from the previous step, we then solve for the image using a SENSE+motion forward model:

$$[\hat{\boldsymbol{x}}] = \underset{\boldsymbol{x}}{\mathrm{argmin}} ||\boldsymbol{s}-\boldsymbol{E}_{\boldsymbol{\theta}}\boldsymbol{x}||_2$$

CNN Training: Our CNN was trained on simulated data, generated from in vivo T₂-weighted RARE/TSE/FSE¹¹ images with TR/TE=6.1s/103ms, in-plane FOV=220x220mm², 4mm slices, 448x448x35mm³ matrix size, 0.5x0.5mm² in-plane resolution, R=2 undersampling, and TF=11. Ten evenly spaced slices from four healthy subjects, each corrupted by 10 different motion trajectories were used as training data (400 examples total). Motion trajectories were taken from AD patient fMRI runs and augmented using shifting and scaling.

Validation: The CNN was applied to simulated motion corrupted slices from a fifth healthy subject to assess the performance on unseen anatomy. For a test slice, twenty NAMER iterations were performed. To compare to standard iterative methods without the CNN, an alternating minimization^4,12 was performed until convergence (about 80 iterations). Lastly, NAMER was applied to an additional two "real" motion cases, where the subjects were asked to shake their heads "no" during the middle of the scan.

Results

Figure 3 shows the performance of the CNN alone to remove image artifacts across the whole brain of an unseen test subject. All slices had reduced image space RMSE, with an average of 3.9%. While the CNN alone removes some motion artifacts, it is incomplete and introduces some blurring.

Figure 4 shows the data-consistency error of the motion search at each iteration of the NAMER and alternating methods. NAMER converges to a high-quality image after five iterations, while the no-CNN method still has significant artifacts. To reach a data-consistency error of 9.8% (close to the SNR limit of the acquisition), NAMER took 6 iterations, whereas the alternating method required 60, leading to a >15x increase in reconstruction time.

Figure 5 shows the image results from two real motion cases. Ringing was reduced for both subjects, and the position coordinates returned from NAMER correspond to the expected motion, based on the instructions given to the subjects.

Discussion and Conclustion

Acknowledgements

References

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