# Hyperspectral Data: Efficient and Secure Transmission
## 2 An Efficient and Secure Transmission Framework
### An Effective Implementation of the Proposed Framework
#### 2.1.1 Reversible Invisible Watermarking Scheme for Hyperspectral Images
Each hyperspectral image is subdivided into sub-images which are denoted as scenes. In detail, a scene is composed by 614 columns, 512 lines (except for the last scene that might have a lower number of lines), and 224 bands. Each pixel is stored as a signed integer and represented with 16 bits. In Table 1, we report for each hyperspectral image (rows) and the number of its scenes (second column). **Dataset 2. ** The second dataset is referred to as the \"CCSDS Dataset\" and it is composed of five calibrated and seven uncalibrated AVIRIS hyperspectral images. This dataset is publicly available, and it is provided by the Consultative Committee for Space Data Systems (CCSDS) Multispectral and Hyperspectral Data Compression [17]. Table 2 shortly reports the key information describing Dataset 2 by showing the number of scenes (second column) and the number of columns (third column), concerning the calibrated and the uncalibrated images (first column). We remark that a pixel of the calibrated and the uncalibrated images is stored by using 16 bits (16-bit signed integer, for the calibrated, and 16-bit unsigned integer, for the uncalibrated), except for the Hawaii and Maine hyperspectral images which have pixels stored by using 12 bits (unsigned) [17]. Each of the hyperspectral images in the Dataset 2 is composed of 512 lines. ### Simulation Results Achieved by the Reversible Invisible Watermarking Scheme

This section outlines the experimental results we have achieved by using our reversible invisible watermarking scheme by considering both Dataset 1 and Dataset 2. Analogously to [18], we have considered the peak-signal-to-noise-ratio (PSNR) [19], to evaluate the distortion between the original image \(HI\) and the watermarked one (i.e., \(HI^{W}\)). The PSNR metric is computed as in Equation (4). \[PSNR(HI,\;HI^{W})=\frac{1}{M}\sum_{i=1}^{M}\Bigg{(}10\log_{10}\Bigg{(}\frac{ \left(2^{15}-1\right)^{2}}{MSE(HI_{(i)},\;HI_{(i)}^{W})}\Bigg{)}\Bigg{)} \tag{4}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperspectral Image** & **Number of Scenes** \\ \hline Cuprite & 5 \\ Jasper Ridge & 6 \\ Low Altitude & 8 \\ Lunar Lake & 3 \\ Moffett Field & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Description of the Dataset 1. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Hyperspectral Image** & **Number of Scenes** & **Columns** \\ \hline Yellowstone (calibrated) & 5 & 677 \\ Yellowstone (uncalibrated) & 5 & 680 \\ Hawaii (uncalibrated) & 1 & 614 \\ Maine (uncalibrated) & 1 & 680 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Description of the Dataset 2. The mean squared error (MSE) instead is defined in Equation (5), in which the notation \(HI_{(i)}(x,y)\) is referred to the pixel at the coordinates \((x,y)\) of the \(i\)th band. \[MSE(HI_{(i)},\;HI_{(i)}^{W})=\frac{1}{WH}\sum_{x=1}^{W}\sum_{y=1}^{H}\left(HI_{( i)}(x,y)-HI_{(i)}^{W}(x,y)\right)^{2} \tag{5}\]

In all our experiments, we have considered two watermarks:

* \(w_{1}\)--Composed by 1120 bits (pseudo-random generated)
* \(w_{2}\)--Composed by 2240 bits (pseudo-random generated). #### 3.2.1 Simulation Results on Dataset 1

In Table 3 we report, in terms of the PSNR metric, the achieved test simulation results by embedding the watermark \(w_{1}\) into Dataset 1. The PSNR value of the watermarked image with respect to the original image is reported for each scene (first column) of Cuprite (on the second column), Jasper Ridge (on the third column), Low Altitude (on the fourth column), Lunar Lake (on the fifth column), and Moffett Field (on the sixth column) hyperspectral images. In Table 4, we report the achieved simulation results by embedding the watermark \(w_{2}\). Figure 2 synthetizes the average PSNR results we have achieved by embedding the watermark \(w_{1}\) (columns in red) and the watermark \(w_{2}\) (columns in blue), by considering Dataset 1.