# Reversible Data Hiding for DICOM Image Using Lifting and Companding
## 6 Performance Evaluation  
The performance of the proposed reversible watermarking scheme is evaluated over various DICOM medical images having diverse image features and characteristics. The test medical images are of size (\(512\times 512\)). All experimentations are evaluated in Pentium 4, with 512 MB RAM and 2.80 GHz processor, by MATLAB 7. The present study uses Mean-Structure-Similarity-Index-Measure (MSSIM) [33] and Peak-Signal-to-Noise-Ratio (PSNR) as distortion measures for the watermarked image. On the other hand, the relative entropy distance (Kullback Leibler distance (KLD)) [3] is used to quantify the security (K) of the proposed scheme. The large Peak-Signal-to-Noise-Ratio (PSNR) and Mean-Structure-Similarity-Index-Measure (MSSIM) values and low-security values of the watermarked medical image represent better imperceptibility and security of the hidden data, respectively [34]. PSNR is defined as:  
\[\text{PSNR}=10\log_{10}\left(\frac{\text{MAX}^{2}}{\text{MSE}}\right) \tag{19}\]  
The symbol MAX represents the maximum gray value of pixel for the DICOM medical image. Mean Square Error (MSE) is represented as:  
\[\text{MSE}=\frac{1}{\text{MN}}\sum_{i=0}^{M-1}\sum_{j=0}^{N-1}[X(i,j)-x^{ \prime}(i,j)]^{2} \tag{20}\]  
where, the symbol 'X' is the gray value of the pixel for the original DICOM host image and 'X' is the gray value of pixel for the watermarked DICOMimage. The symbol '\(M\)' and '\(N\)' are the height and width of the host image, respectively. MSSIM [33] is defined as:  
\[\text{MSSIM}\left(P,\overline{P}\right)=\frac{1}{M^{\prime}}\sum_{j^{\prime}= 1}^{M^{\prime}}SSIM\left(P_{j^{\prime}},\overline{P_{j^{\prime}}}\right) \tag{21}\]  
where,  
\[SSIM\left(P,\overline{P}\right)=\left[lu\left(P,\overline{P}\right)\right]^{ \alpha}\left[co\left(P,\overline{P}\right)\right]^{\beta}\left[sI\left(P, \overline{P}\right)\right]^{\gamma} \tag{22}\]  
where the symbol '\(P\)' and '\(\overline{P}\)' are the original and the distorted DICOM image signals, respectively. The symbol '\(M\)' represents the number of local windows in the DICOM image. The symbol '\(P_{j^{\prime}}\)' and '\(\overline{P}_{j^{\prime}}\)' are the image information at the j'-th local window. The functions \(\text{lu}\left(P,\overline{P}\right)\), \(\text{co}\left(P,\overline{P}\right)\) and \(\text{st}\left(P,\overline{P}\right)\) are the luminance, contrast, and structure comparison functions respectively. The symbols \(\alpha\), \(\beta\), and \(\gamma\) {where \(\alpha>0\), \(\beta>0\), \(\gamma>0\)} are the parameters used to control the relative weight of the above components. The KLD (D(a\|b)) is represented as [3]:  
\[D(a\|b)=\sum_{x\in X}a(x)\log\frac{a(x)}{b(x)}=E_{a}\log\frac{a(X)}{b(X)} \tag{23}\]  
\[\text{with }0\log\frac{0}{b}=0,\text{ a }\log\frac{a}{0}=\infty\]  
where the symbol \(a(x)\) and \(b(x)\) representsthe probability distribution functions (PDF) of the random variables \(R\) (i.e., original host image) and \(S\) (i.e., watermarked image), respectively. The symbol \(E_{a}\) represents the expectation concerning the joint distribution 'a'. If \(a(X)=b(X)\) the security value is always non-negative or zero. On the other hand, the security value may be assumed to be '\(K\)' if \(D\) (\(a\|b)\leq K\)[3]. In the proposed scheme, the normalized cross-correlation (NCC) is used to quantify the quality of the extracted watermark [34]. The NCC value between the original watermark image (\(W\)) and the extracted watermark image (\(W^{\prime}\)) is represented as:  
\[\text{NCC}=\frac{\sum_{i}\sum_{j}W_{ij}W^{\prime}{}_{ij}}{\sum_{i}\sum_{j} \left(W_{ij}\right)^{2}} \tag{24}\]  
image is decreased. It is also seen that due to the increase of payload size, there is no such deviation in structural values of watermarked images. It is quite interesting to see that for MRI-2 image, and there is no change in structural value even if the payload size is increased to 65,536 bits. It is also to be noted that with the increase in payload size, the value of KLD is also increased.