Table 1.

Workflow for Simultaneous CT-MRI Image Reconstruction

Inputs:	CT projection data f and MRI k-space data g
Reconstruction:	1. Reconstruct a CT image uCT from f by Eq. (5);
	2. Reconstruct an MRI image uMRI from g by Eq. (6);
	3. k = 0;
	4. Loop until meeting the stop criteria
	5. Transform CT-MRI datasets TCT–MRI by given uMRI and uCT ;
	6. Estimate the corresponded CT-MRI image ${\mathbf{u}}_{CT}^{est}$ & ${\mathbf{u}}_{MRI}^{est}$ according to uMRI & uCT aided by TCT–MRI using the SC method (Table 2);
	7. Reconstruct the CT image with ${\mathbf{u}}_{CT}^{est}$ and f by Eq. (7);
	8. Reconstruct the MRI image with ${\mathbf{u}}_{MRI}^{est}$ and g by Eq. (8);
	9. k = k + 1;
	10. end