Statistical testing of LPC versus Burg algorithm
For the assessment of statistical significance of the effect of the AR model estimator (LPC versus Burg algorithm), the Wilcoxon signed rank test was employed using the following hypotheses:
- H0: Burg algorithm and LPC lead to results with the same median,
- HA: Burg algorithm leads to results with higher median.
This was performed separately for each inpainting method, AR model order, and evaluation metric (SDR, PEMO-Q ODG).
The p-value displayed in the tables below indicate the rejection of the null hypothesis, i.e., p-value < 0.05 implies that the data feature enough evidence to reject the equality of the medians in favor of the alternative hypothesis HA (at the significance level of 5%). On the other hand, p-value > 0.05 means the test is inconclusive.
| evaluation by SDR | 256 | 512 | 1024 | 2048 | 3072 |
|---|---|---|---|---|---|
| extrapolation-based | 1.06e-21 | 2.12e-22 | 2.12e-22 | 2.12e-22 | 3.58e-20 |
| Janssen, gap-wise | 2.16e-09 | 3.89e-13 | 5.54e-10 | 0.03 | 0.97 |
| Janssen, Hann window | 7.82e-05 | 6.19e-4 | 0.90 | 1.00 | 1.00 |
| Janssen, rect. window | 6.69e-11 | 4.67e-06 | 0.39 | 0.99 | 1.00 |
| evaluation by ODG | 256 | 512 | 1024 | 2048 | 3072 |
|---|---|---|---|---|---|
| extrapolation-based | 6.35e-22 | 2.12e-22 | 2.12e-22 | 2.12e-22 | 3.57e-18 |
| Janssen, gap-wise | 8.94e-13 | 1.25e-18 | 1.86e-20 | 3.42e-16 | 5.10e-06 |
| Janssen, Hann window | 0.20 | 0.09 | 0.06 | 1.00 | 1.00 |
| Janssen, rect. window | 2.11e-22 | 1.84e-18 | 0.02 | 0.99 | 0.99 |
To assess the superiority of LPC in some cases, we performed the same test using a different altarnative hypothesis:
- H0: Burg algorithm and LPC lead to results with the same median,
- HA: Burg algorithm leads to results with lower median.
In this case, p-values < 0.05 imply statistical significance of the LPC surpassing the Burg algorithm (at the significance level of 5%).
| evaluation by SDR | 256 | 512 | 1024 | 2048 | 3072 |
|---|---|---|---|---|---|
| extrapolation-based | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Janssen, gap-wise | 1.00 | 1.00 | 1.00 | 0.97 | 0.03 |
| Janssen, Hann window | 1.00 | 1.00 | 0.10 | 4.06e-18 | 3.22e-14 |
| Janssen, rect. window | 1.00 | 1.00 | 0.61 | 0.01 | 7.01e-4 |
| evaluation by ODG | 256 | 512 | 1024 | 2048 | 3072 |
|---|---|---|---|---|---|
| extrapolation-based | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Janssen, gap-wise | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| Janssen, Hann window | 0.80 | 0.91 | 0.94 | 8.78e-4 | 4.67e-3 |
| Janssen, rect. window | 1.00 | 1.00 | 0.98 | 0.01 | 8.69e-3 |