# Image Completion with Hybrid Interpolation in Tensor Representation
## 4 Results
### Discussion  
The experiments were carried out for typical but challenging image completion problems. In test A, we knew only 10% of the pixels in the \"Barbara\" image, and the aim was to recover the 90% \begin{table}
\begin{tabular}{c c c c c} \hline
**Algorithm/Test** & **Test A** & **Test B** & **Test C** & **Test D** \\ \hline FAN & 0.25 \(\pm\) 0.08 & 0.25 \(\pm\) 0.06 & 0.24 \(\pm\) 0.04 & 0.2 \(\pm\) 0.04 \\ \hline EFAN & 0.06 \(\pm\) 0.01 & 0.06 \(\pm\) 0.01 & 0.15 \(\pm\) 0.01 & 0.07 \(\pm\) 0.01 \\ \hline SmPC-QV & 534.67 \(\pm\) 91.82 & 579.12 \(\pm\) 109.36 & 416.68 \(\pm\) 82.97 & 507.74 \(\pm\) 101.19 \\ \hline LRTV & 876.64 \(\pm\) 89.25 & 943.6 \(\pm\) 78.45 & 966.72 \(\pm\) 87.01 & 977.86 \(\pm\) 117.85 \\ \hline C-SALSA & 73.87 \(\pm\) 17.08 & 86.47 \(\pm\) 22.52 & 66.33 \(\pm\) 18.84 & 354.58 \(\pm\) 91.99 \\ \hline TMac-inc & 122.37 \(\pm\) 21.75 & 120.8 \(\pm\) 40.98 & 440.05 \(\pm\) 54.35 & 193.22 \(\pm\) 23.29 \\ \hline fALS & 545.39 \(\pm\) 63.67 & 478.98 \(\pm\) 47.47 & 879.41 \(\pm\) 74.83 & 206.23 \(\pm\) 74.93 \\ \hline KA-TT & 433.8 \(\pm\) 81.18 & 379.54 \(\pm\) 63.55 & 392.59 \(\pm\) 54.09 & 419.3 \(\pm\) 70.94 \\ \hline TI-IC(Exp) & 3.77 \(\pm\) 1.03 & 1.39 \(\pm\) 0.17 & 133.14 \(\pm\) 10.92 & 15.08 \(\pm\) 1.97 \\ \hline TI-IC(Exp) & 1.7 \(\pm\) 0.12 & 1.14 \(\pm\) 0.04 & 15.39 \(\pm\) 0.56 & 2.81 \(\pm\) 0.1 \\ \hline TI-IC(Poly) & 0.57 \(\pm\) 0.11 & 0.13 \(\pm\) 0.02 & 1.73 \(\pm\) 0.11 & 0.71 \(\pm\) 0.1 \\ \hline TI-IC(Poly) & 0.49 \(\pm\) 0.03 & 0.36 \(\pm\) 0.01 & 0.58 \(\pm\) 0.02 & 0.49 \(\pm\) 0.01 \\ \hline TI-IC & 6.01 \(\pm\) 1.49 & 2.91 \(\pm\) 0.78 & 406.75 \(\pm\) 51.51 & 24.59 \(\pm\) 4.77 \\ \hline TI-IC & 1.96 \(\pm\) 0.05 & 1.19 \(\pm\) 0.04 & 40.98 \(\pm\) 1.79 & 4.15 \(\pm\) 0.18 \\ \hline \end{tabular}
\end{table} 
Table 1: Mean runtime (in seconds) of the algorithms and the corresponding standard deviations for each test case. An asterisk denotes the use of parallel processing with a parallel pool of workers in MATLAB. Figure 6: Box-plots of signal-to-interference ratio (SIR) performance for the tests (**A–D**) with the algorithms 1 = FAN, 2 = EFAN, 3 = SmPC-QV, 4 = LRTV, 5 = C-SALSA, 6 = TMac-inc, 7 = fALS, 8 = KA-TT, 9 = TI-IC(Exp), 10 = TI-IC(Poly), 11 = TI-IC. missing pixels. The results illustrated in Figures 2 and 6A show that good quality reconstructions were obtained when the EFAN, SmPC-QV, fALS, KA-TT, TI-IC(Exp), and TI-IC algorithms were used, but the image recovered with TI-IC had the highest SIR score. TI-IC was also quite fast in this test (see Table 1). It lost in the runtime category only to FAN and EFAN, but its parallel version TI-IC * ) was more than 250 times faster than SmPC-QV. The latter performs the CP decomposition, but the difference in computational speed comes from the fact that in our method, the factor matrices are precomputed, and only the core tensor in the Tucker decomposition is estimated using the data. The results obtained in Test B are presented in Figures 3 and 6B. They confirm the conclusions drawn from Test A, but it should be noted that TI-IC strengthened its leading position in the SIR performance. Moreover, its runtime was shorter than that in the previous test because only 5% of the entries were known, and hence the system matrix in (19) was smaller. Test C compared algorithms for the completion of many small-scale missing regions (holes), distributed across the image. The results presented in Figures 4 and 6C show that EFAN and SmPC-QV failed to provide satisfactory reconstructions in this test, but TI-IC outperformed the other algorithms considerably. Obviously, a lower number of missing pixels in the image to be completed results in a noticeable increase in the runtime, but it was still below the runtime of low-rank tensor completion methods, such as SmPC-QV, TMac-inc, fALS, and LRTV. In Test D, only 50 % of pixels were unknown, but not all the tested algorithms handled this case well.