# Intra Prediction-Based Hologram Phase Component Coding Using Modified Phase Unwrapping
## 4 Experiment and Result
### Coding Result
ratio of 100:1, the vertical unwrapping method shows better performance over 2 dB in phase and reconstruction results than other methods. Compared to the JPEG2000 and the HEVC Intra, our method shows a difference of almost 4 dB in all of the phase and reconstruction results. In the results of real and imaginary parts, shown in Figure 16c,d, this trend is almost the same. In particular, in the case of using the proposed method, it can be seen that the PSNR of the real part and the imaginary part are kept almost similar. The hologram phase information may vary depending on the hologram generation method and the amount of random phase. For these various phase information, the segment and CU size having the most optimal compression efficiency may differ. After setting  
Figure 16: Performance comparison of the various methods: (**a**) phase, (**b**) reconstruction, (**c**) real, and (**d**) imaginary part. Figure 15: Compression results with the diagonal unwrapping: (**a**) phase, (**b**) reconstruction result. the segment and the CU size in advance within the size range dependent on the CU size of HEVC, the greedy method that obtains the best compression efficiency result after coding the phase information under various conditions can be applied. The numerical reconstruction result of the phase information is shown as an image. We performed experiments using holograms provided by JPEG Pleno. Among them, the resulting images for the Horse [18] and Dices [20; 21] holograms are shown in Figures 17-19. Figure 17 is the reconstruction result of the original hologram. The resolution of Horse, which is the Fresnel hologram method, is 972 \(\times\) 972 and the pixel pitch is 6.4 \(\upmu\)m. It has only the red channel of 632.8 nm wavelength, and the reconstruction distance is 14 cm. Dices, which is an angular spectrum method, has a size of 1920 \(\times\) 1080 and a pixel pitch of 6.4 \(\upmu\)m. The wavelengths for the red, green, and blue channels are 640, 532, and 483 nm, respectively. Its reconstruction distance is 0.327 cm. The reconstruction for the Fresnel diffraction method is defined by Equation (1). \(\Delta x\) and \(\Delta y\) are sampling periods for the \(x\)-axis and \(y\)-axis, respectively, and the number of samplings is M and N. \(H(p,q)\) represents a hologram, and \(k_{0}\) represents a wave number. \((m,n)\) and \((p,q)\) are indexes of samples in the spatial domain and Fourier domain, respectively. \[O(p,q)=\frac{ik_{0}e^{-\beta_{0}z}}{2\pi z}exp\bigg{\{}-j\pi\lambda z\bigg{[} \bigg{(}\frac{p}{M\Delta x}\bigg{)}^{2}+\bigg{(}\frac{q}{N\Delta y}\bigg{)}^{ 2}\bigg{]}\bigg{\}}\times IDFT_{2D}\bigg{\{}H(m,n)exp\bigg{[}\frac{-jk_{0}}{2 \pi}\bigg{(}m^{2}\Delta_{x}^{2}+n^{2}\Delta_{y}^{2}\bigg{)}\bigg{]}\bigg{\}} \tag{1}\]  
The reconstruction for the angular spectrum method is defined by Equation (2). \(k_{x}\) and \(k_{y}\) are spatial radian frequencies, respectively. Since \(\Delta_{kx}\) and \(\Delta_{ky}\) are defined as frequency resolution, \(\Delta_{kx}=2\pi/M\Delta_{x}\) and \(\Delta_{ky}=2\pi/M\Delta_{y}\). Equations (1) and (2) are described in detail in [22]. \[O(p,q)=DFT_{2D}\bigg{[}IDFT_{2D}H(m,n)*exp\bigg{[}-jk_{0}z\sqrt{1-\frac{(p \Delta_{kx})^{2}}{k_{0}^{2}}-\frac{(q\Delta_{ky})^{2}}{k_{0}^{2}}}\bigg{]} \bigg{]} \tag{2}\]  
Figure 18 is for the Horse hologram, and Figure 19 is for the Dices hologram. In Figures 18 and 19, each subfigure includes the result of the JPEG2000, the HEVC Intra, and the proposed method. In both figures, (a) and (b) are reconstruction images for compression ratios of 50:1 and 100:1, respectively. At a compression ratio of 50:1 in the two images, it is difficult to visually confirm the difference in quality. In Figure 18, it can be clearly seen that the proposed method at a compression ratio of 100:1 shows better visual quality than other methods. In Figure 19, it can be seen that the color is deteriorated in the compression result by JPEG2000.