# A Novel PCA-Based Method for PRNU Distillation to the Benefit of Source Camera Identification
## 4 Experiment and Evaluations
### Performance Evaluation  
To demonstrate the performance of our proposed scheme, we use two evaluation criteria: the overall receiver operating characteristic (ROC) evaluation statistics and the calculated Kappa statistic based on the confusion matrix. To obtain the overall ROC curve, for a given detection threshold, true positives and false positives were recorded for each camera, and these numbers were then summed and used to calculate the true positive rate (TPR) and false positive rate (FPR). Specifically, since each camera captures exactly the same number of images, we can simply calculate the TPR and FPR thresholds as follows. \[TPR =T_{TP}\bigg{/}(N_{TP}+N_{FN}) \tag{17}\] \[FPR =T_{FP}\bigg{/}(N_{FP}+N_{TN})\]  
where \(N_{TP},N_{FN},N_{FP}\) and \(N_{TN}\) represent the number of intraclass samples judged as intraclass samples, intraclass samples judged as interclass samples judged as intraclass samples and interclass samples judged as interclass samples, respectively. After calculating the detection threshold of the PCE according to Equation (16), the overall ROC curve can be obtained by varying the detection threshold from the minimum to maximum values. To obtain the confusion matrix, we calculate the similarity between the PRNU of each query image in Table 1 and the reference PRNU of each camera, then the camera with the highest similarity corresponding to this image is identified. The value of each element \(\mathbf{M}(i,j)\) in the confusion matrix indicates the number of images captured by camera \(i\) that are categorized as captured by camera \(j\). In other words, the values along the main diagonal indicate the number of correct categorizations. Each confusion matrix can be reduced to a single statistic, the Kappa statistic, i.e.,  
\[Kappa=(o-\varphi)\bigg{/}(T-\varphi), \tag{18}\]  
where \(o\) is the number of images correctly categorized in the camera, i.e., the trace of the confusion matrix, \(T\) is the total number of query images, and \(\varphi\) is the number of correctly predicted categories. \[\varphi=\sum_{c=1}^{C}\frac{\sum_{i=1}^{C}M(c,i)\sum_{j=1}^{C}M(j,c)}{T}, \tag{19}\]  
The Kappa statistic measures the inconsistency between the observations and random guesses. Therefore, the larger the values, the better the performance, with 1 indicating perfect performance. The most computationally costly resource of the proposed scheme is the cost of the LPM and PCA transformation, and thus, its complexity mainly depends on two parameters: the matching window size \(K\) and the training block size \(L\). Suppose \(n\) training samples are selected, dataset \(K\) is of dimension \(n\times k^{2}\). The singular value decomposition (SVD) is used in the PCA transformation to obtain the \(K^{2}\times K^{2}\) covariance matrix. In order to estimate the interfering noise from the PRNU noise by using PCA, we need to construct a set of training samples of the PRNU noise. In the experiment of extracting scene details, we need to use the complete \(L\times L\) block centred on the given pixel as a training block to find the training sample. We calculate the similarity between the \(K\times K\) block centred on the given pixel and all the \(K\times K\) blocks within the training block, then choose high-similarity blocks as the training sample. We made reference to the parameters \(K=5\), \(L=41\) and \(S=9\) in [6; 19]. We selected the optimal value of \(K\) and \(L\) through ablation experiments. We set \(L=41\), varied \(K\) from 3 to 9, and showed the results on the block size of \(128\times 128\) pixels. It is easy to see from Figure 3 that varying \(K\) has a trivial effect on the final camera identification performance. Taking the false positive rate \(FP=0.01\) for example, \(K=3\), 5, 7, and 9 achieve true positive \(TP=0.699\), 0.705, 0.697, 0.695. Based on the results of the above experiment, we set \(K=5\), varied \(L\) from 21 to 51. In Figure 4, the ROC curves of the camera identification performance are weakly affected by the change in \(L\).