# Intra Prediction-Based Hologram Phase Component Coding Using Modified Phase Unwrapping
## 3 Phase Compression
### Intra Prediction with Unwrapping  
We propose a phase unwrapping technique that can show the highest correlation between the phase component of a hologram and Intra prediction through numerous trials and experiments. This method is simple, but it is a way to overcome the limitation of phase unwrapping for compression shown in Section 2.2. The proposed method is shown in Figure 8a, and the structure of the Intra prediction block we intended is shown in Figure 8b. \(R\) and \(P\) in Figure 8b represent the reference block and the prediction block in Figure 7, respectively. Phase linearity increases due to the phase unwrapping technique, but there is a problem in that the error per bit increases in lossy processing such as compression. Therefore, we proposed a method to increase the linearity and decrease the error per bit. That is, it can be regarded as a method that considers the trade-off relationship between linearity and compression efficiency. As shown in the algorithm in Figure 8a, the unwrapping method is limited to the preset threshold (\(4\pi\), \(8\pi\), \(16\pi\), and \(32\pi\)). This differentiates it from the general unwrapping method, which has an infinite range. Linearity is given by dividing \(2\pi n\) by a certain interval (the value of unwrap in Figure 8a) and adding it to the original phase.  
As described in Section 3.1, the phase unwrapping is applied in consideration of the characteristics of the HEVC Intra coding. In order to simply apply unwrapping and increase the effect of directional prediction in the Intra coding, we propose a modified unwrapping technique in three directions. One object point forms a fringe pattern with a multiple circle shape on the 2D hologram plane. If circle-shaped fringe patterns with the same shape in all directions overlap very much in the case of multiple object points, it may be predicted that the resulting pattern does not have a dominant directionality in any particular direction. Figure 9 shows the results of measuring the HEVC Intra mode while rotating the hologram around the center. The graph in Figure 9 shows that the angular directions in the HEVC Intra prediction are variously distributed within  
Figure 7: HEVC Intra coding, (**a**) reference samples Rx,y used in prediction to obtain predicted samples \(P_{x,y}\) for a block of size \(N\times N\) samples, (**b**) Figure 2. HEVC angular Intra prediction modes numbered from 2 to 34 and the associated displacement parameters. H and V are used to indicate the horizontal and vertical directionalities, respectively, while the numeric part of the identifier refers to the pixels’ displacement as \(1/32\) pixel fractions [19].  
the hologram. In the graph of Figure 9, the angular direction number is the same as Figure 7b. We propose an algorithm that manipulates the hologram using the modified phase unwrapping so that HEVC Intra prediction can be performed well. Therefore, it is possible to select some of the angular modes used in the Intra prediction. We select the vertical, horizontal, and diagonal directions corresponding to 0 degrees (180 degrees), 45 degrees (225 degrees), and 90 degrees (270 degrees), and then manipulate the hologram using a modified unwrapping technique.  
The three modified unwrapping methods are shown in Figure 10. Figure 10a-c show how to unwrap the phase in vertical, horizontal, and diagonal directions, respectively. The unwrapping proceeds from the dark to the bright region. That is, the brightness can be viewed as the magnitude of the dynamic range of the unwrapped phase. Each figure in Figure 10 consists of a total of 16 blocks. Each block corresponds to a CU in the HEVC codec. Considering HEVC Intra prediction, we divide the block as shown in Figure 10 to the same size as the CU used for Intra prediction, and apply phase unwrapping.  
Figure 8: Proposed unwrapping algorithm (**a**) the pseudo-code, (**b**) the segments for the intra prediction.  
Figure 9: Distribution of angular directional modes.