# Low Tensor Rank Constrained Image Inpainting Using a Novel Arrangement Scheme
## 4 Experimental Results and Analyses
### Missing Ratio of 90%  
To further test the effectiveness of our method under 90% missing entries, we conducted comparative experiments with the state-of-the-art TTC and TCTV methods [50] based on tensor TT decomposition, the CFN-RTC method [33] based on TR decomposition, and the RNC-FCTN method [32] based on FCTN decomposition. For fairness, we directly used the codes and images provided by the TTC and TTCTV methods in [50] and [[https://github.com/IRENEKO/TTC](https://github.com/IRENEKO/TTC)]([https://github.com/IRENEKO/TTC](https://github.com/IRENEKO/TTC)), where the related parameters are also set by their code. We directly used the codes provided by the CFN-RTC and RNC-FCTN methods, set the optimal parameters such as tensor rank, and arranged the input images according to the size in their codes. The original image is shown in Figure 13. At a random 90% missing entries, the PSNR and SSIM of the observed image were 5.7036 dB and 3.56%, respectively. Comparing ten methods, including TTC, TTCTV, CFN-RTC, RNC-FCTN, TTLR, UnfoldingLR, TTLRTV, tSVDLRTV, and UnfoldingLRTV, the visual results are shown in Figure 13, and the numerical indicators are shown in Table 6.  
Experiments showed that, under high missing rates, there was significant visual pollution in the recovered images of the ten methods. However, compared to the original polluted image, there was a significant improvement, and there were differences in the recovered details among the ten methods. The CFN-RTC, TTC, TTCTV, and tSVDL methods had significant grid-like pollution in repairing images, while the TTLR and UnfoldingLR methods had significant block-like pollution. The RNC-FCTN method had the worst visual effect, but this does not mean that this method has no advantage in processing high-dimensional videos or hyperspectral video (HSV) data. We only forced it to process image data in this experiment, and the results showed that it had a certain effect. The TTLRTV, tSVDLRTV, and UnfoldingLRTV methods had better visual effects than the other methods, but there was significant pulse-like noise in the details.  
In terms of numerical indicators, the TTC and TTCTV methods could only improve PSNR and SSIM by about 3 dB and 14%, respectively, which is clearly not advantageous compared to our five methods. Our five methods could improve PSNR and SSIM by more than 13 dB and 40%, respectively. The CFN-RTC method could also achieve close improvements.  
The RTC-FCTN method is based on FCTN decomposition, while the CFN-RTC method is based on TR decomposition. FCTN is an improvement of TR decomposition, but the experimental results of the two methods were different. The RNC-FCTN method was directly used to process high-dimensional data, while in the CFN-RTC method experiment, the authors first simply reshaped low-dimensional data into high-dimensional data, which enabled the TR decomposition tool to be applied to low-dimensional data processing.  
Analyzing the reasons for the above experimental results, our method may greatly benefit from using more flexible data rearrangement schemes, which make low-rank approximation more sufficient and are based on more effective distributed iterative solving algorithms. Moreover, the TTC and TTCTV methods are not based on the inpainting model established by decomposing tensors into multiple TT matrix forms but rather on directly decomposing tensors into less precise forms of multiple core tensors.