Table 2.
Inversion results for unknown m0 and p for test-case TC (d). eι are the relative errors in parameter ι. Atlas (*) are the different atlases used. True atlas is the ground truth m0. u* is the ground truth displacement norm in number of voxels, ∥g∥2 is the norm of the final gradient, and μT,L2 is the relative error in the final tumor concentration. The results for other test-cases are reported in supplementary Table S2.
| ID | Test-case | eγ | eρ | eκ | ∥u*∥∞ | eu | ∥g∥2 | μ T,L2 |
|---|---|---|---|---|---|---|---|---|
| TC (d) | True atlas | 2.48E−2 | 1.81E−1 | 2.54E−1 | 14.9 | 2.91E−2 | 5.75E−4 | 2.05E−1 |
| Atlas (1) | 1.63E−2 | 2.15E−1 | 2.65E−1 | 14.9 | 1.21E−1 | 2.71E−4 | 3.37E−1 | |
| Atlas (2) | 1.13E−1 | 2.35E−1 | 9.27E−2 | 14.9 | 2.00E−1 | 6.85E−4 | 3.04E−1 | |
| Atlas (3) | 2.50E−1 | 2.06E−1 | 5.46E−1 | 14.9 | 2.39E−1 | 5.43E−4 | 2.79E−1 |