Algorithm 1.

Pseudo CT prediction using anatomic signature and joint dictionary learning.

1. For each training MR image patch $I^{\mathrm{MR}}$, extract the multiscale and multilevel 3-D RILBP feature $f^{\mathrm{MR}}$.

2. Use fuzzy C-means to segment each corresponding CT $I^{\mathrm{CT}}$ into three labels that represent the CT values in the range of bone, soft-tissue and air.

3. For the coupled training MRI features and corresponding CT labels, apply LASSO logistic regression Eq. (1) to select the informative features as an anatomic signature.

4. Use Fisher’s score47 to measure the discriminant power of the anatomic signature to separate bone, air and soft-tissue, and normalize to $\omega$ such that $\sum _{}^{}{\omega }_i=1$.

5. For each new arrival MRI image patch $I_i^{\mathrm{MR}}$, select its similar patches $I_{ij}^{\mathrm{MR}}$ from the training patches by computing the weight $w_{ij}$ from Eq. (2), and sorting the K-nearest patches by Eq. (3).

6. For the anatomic features $f_{ij}^{\mathrm{MR}}$ of $I_{ij}^{\mathrm{MR}}$ and corresponding CT voxels $y_{ij}^{\mathrm{CT}}$, initialize the coupled dictionaries: ${\widehat{D}}^{\mathrm{MR}}=\{f_{ij}^{\mathrm{MR}}|j\in N_{k_x\times k_y\times k_z}(i)\backslash \{i\}\}$ and ${\widehat{D}}^{\mathrm{CT}}=\{y_{ij}^{\mathrm{CT}}|j\in N_{k_x\times k_y\times k_z}(i)\backslash \{i\}\}$.

7. Use joint dictionary learning [Eq. (4)] to train the coupled dictionary $(D^{\mathrm{MR}},D^{\mathrm{CT}})$.

8. For each new arrival MRI patch, use Eq. (5) to obtain the sparse representation of learned dictionary $D^{\mathrm{MR}}$, and then use Eq. (6) to reconstruct the pseudo CT intensity.