Kamlesh Pawar^{1,2}, Gary F Egan^{1,2,3}, and Zhaolin Chen^{1,4}

^{1}Monash Biomedical Imaging, Monash University, Melbourne, Australia, ^{2}School of Psychological Sciences, Monash University, Melbourne, Australia, ^{3}ARC Centre of Excellence for Integrative Brain Function, Monash University, Melbourne, Australia, ^{4}Department of Data Science and AI, Faculty of Information Technology, Monash University, Melbourne, Australia

Deep learning (DL) models for accelerated image reconstruction involves retrospective undersampling of the fully sampled k-space data for training and validation. This strategy is not a true reflection of real-world data and in many instances, the input k-space data is corrupted with artifacts and errors, such as motion artifacts. In this work, we propose to improve existing methods of DL training and validation by incorporating a motion layer during the training process. The incorporation of a motion layer makes the DL model aware of the underlying motion and results in improved image reconstruction in the presence of motion.

Our model is built upon the end-to-end variational network

$$ k^{t+1}=k^{t} - \eta^{t}M(k^{t}-\hat{k})+R^{t}(k^{t}) \quad [1]$$

where, $$$k^{t}$$$ is current k-space, $$$k^{t+1}$$$ is updated k-space, $$$\hat{k}$$$ is acquired k-space, $$$\eta^{t}$$$ is a learnable data consistency parameter, $$$M$$$ is sampling mask with ones at the sampling locations and $$$R^{t}$$$ is the reconstruction CNN (Figure.1e). Eq.1 is equivalent to one step of gradient descent. The reconstruction CNN proceeds as follows: (i) uses intermediate k-space, (ii) performs the inverse Fourier transform, (iii) combines the multi-channel images to a complex-valued image using the sensitivity maps estimated from the sensitivity maps estimation (SME) network (Figure 1f), (iv) the combined complex-valued image is processed through a Unet, (v) the processed image is converted back to multi-channel k-space and (vi) data consistency (DC) is enforced (Figure 1c). To make the variational network ‘motion aware’ we propose to incorporate a motion layer (MS) Figure 1d) and motion informed data consistency parameter estimator (MIDCP) (Figure 1b)

As shown in Figure 1(a-b), the introduced MIDCP layer takes the intermediate k-space and learns a data consistency parameter using a CNN, thus Eq.1 is modified for VarnetMi as follows:

$$k^{t+1}=k^{t} - H^{t}(k^{t})\;M(k^{t}-\hat{k})+R^{t}(k^{t}) \quad [2]$$

where, $$$H^{t}$$$ is a CNN (Figure 1b) that takes k-space and predicts a single parameter for data consistency.

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DOI: https://doi.org/10.58530/2022/4691