## 4 Results and Discussion  
In our work, ten pairs of compressed and uncompressed phase-only holograms (\(1024\times 1024\) pixel size) calculated from ten different object images (\(512\times 512\) pixel size) with error diffusion method were employed as the training holograms (Figure 5). Two compressed phase-only holograms generated from \"Pepper\" and \"Cameraman\" images, respectively, were employed as the test holograms (Figure 6). Data augmentation was performed: firstly, we rotated the training images by \(90^{\circ}\), \(180^{\circ}\) and \(270^{\circ}\), respectively; and, secondly, we flipped them horizontally. Taking into account the training complexity, the small patch training strategy was adopted, so that training images were split into \(31\times 31\) patches with the stride of 10 and there were \(960,384\) training sub-images in total. Since different holograms usually have many similar image blocks and fringe patterns, the replication properties in hologram images allowed a small number of examples to contain most universal hologram features, which has been revealed in previous works [52]. Hence, the total training sub-images was sufficient for our proposed four-layer network. In this work, stochastic gradient descent backpropagation solver was used with the batch size 128. The initial learning rate was 0.0001 and decayed every five epochs by a factor of 10. There were 25 epochs in total. We used the deep learning platform caffe [53] on an NVIDIA GTX TITAN X GPU with 3072 CUDA cores and 12 GB of RAM to implement all the operations in our network. The training time of a four-layer network was 5 h and the test time for an image with \(512\times 768\) was around 0.32 s.  
In the computer calculation of phase-only holograms, the optical wavelength of illumination light was set to be 532 nm, the pixel size was 8 um and the distance between object image and hologram plane was 0.3 m or 0.5 m. The ten training holograms and two testing holograms were then compressed by JPEG when the quality factor is set to 1. The JPEG compressed hologram was restored by our proposed deep convolutional network. One example of the original hologram, JPEG compressed hologram and restored hologram with our proposed scheme is shown in Figure 7. It can be observed  
Figure 4: (**a**) Structure of deep convolutional network for the quality enhancement of JPEG compressed holograms in our work; and (**b**) overall flowchart of our proposed “JPEG+deep learning” hologram compression scheme. that some high frequency patterns are deteriorated in the hologram after JPEG compression and restored to certain extent after the quality enhancement using our proposed network. The reconstructed images from original uncompressed holograms, JPEG compressed holograms and restored holograms were compared in numerical simulations. The reconstructed images are shown in Figure 8. The PSNR, SSIM [54], multi-scale SSIM (MS-SSIM) [55], visual information fidelity (VIF) [56] and information fidelity criterion (IFC) [57] values of the reconstructed results from compressed holograms and restored holograms, in comparison with the reconstructed results from uncompressed holograms, are presented in Table 1. The compression ratio is approximately 7 and data size of original hologram, 1024 KB (1 MB), is reduced to around 142 KB to 144 KB after JPEG compression. All these assessment values reveal that our proposed scheme can significantly enhance the reconstructed image quality from JPEG compressed holograms.