## 1 Introduction  
Computer Generated Holography (CGH) allows the recording and reconstruction of a desired complex light wavefront including both amplitude and phase information. With the development of computer and optical technologies, CGH has been extensively applied in many fields such as three-dimensional dynamic holographic display [1; 2; 3], holographic projection [4; 5; 6; 7], virtual and augmented reality [8; 9], optical tweezers [10] and optical information security [11; 12]. The research works on CGH generation, conversion and compression algorithms receive much attention in the past decade. For example, the enormous amount of calculation in the generation of a complex hologram from a 3D object model consisting of many points is a huge challenge and the fast CGH calculation problem has been investigated from different perspectives [13; 14; 15; 16; 17]. Another major concern is that holographic display devices such as spatial light modulator (SLM) usually cannot display both the amplitude and phase part of a complex hologram simultaneously. Fast and high-quality phase-only hologram calculation from an object image is favorable for commonly used phase-only type SLMs. A phase-only hologram (Figure 1) can be calculated from an object image with various methods such as Gerchberg-Saxton iterative algorithm [18; 19; 20], error diffusion algorithm [21; 22; 23; 24], random phase mask method [25; 26; 27] and down-sampling mask method [28; 29]. Compared with other methods, error diffusion method [21; 22; 23; 24] has several advantages including no forward and backward field propagation, reduction of high frequency noise in the result and direct converting a complex hologram into a phase only one [8]. In this paper, the error diffusion method is employed for the computer generation of phase-only holograms from object images. In addition to the numerical generation of complex or phase-only holograms, the compression of hologram data is a critical issue. Since the unit pixel size of a hologram is typically rather small (a few micrometers), the entire hologram may contain a huge number of pixels and demands considerable storage cost and transmission bandwidth. It is necessary to develop efficient hologram compression algorithms to reduce the size of data representing a hologram. In the past decade, much research effort has been made on hologram compression [30; 31; 32; 33; 34] and a literature review can be found in [30]. In essence, a hologram can be regarded as a special kind of two-dimensional (2D) image. For natural 2D images (e.g., photographs), standardized image compression algorithms such as JPEG [35] have been widely employed. However, some image properties of holograms significantly differ from photographs. For example, a photograph is usually locally smooth while a hologram consists of many high-frequency fringe patterns. Consequently, JPEG compression often cannot give optimal compression performance for holograms [30]. Instead of directly adopting JPEG standard, many customized compression algorithms are proposed for holograms such as Fresnelets [31], Wavelet-Bandelelets Transform [32], vector quantization [33], enhanced wavelet transform [34] and rational covariance extension approach [36; 37]. These customized hologram image compression methods can yield very satisfactory performance for certain types of holograms. However, on the downside, these customized algorithms are not compatible with commonly used JPEG standard, which is supported very extensively by almost every computer system and digital device while these customized compression methods are not very generally adopted. A hologram compression method is very favorable if it has compatibility with JPEG standard and can achieve good compression efficiency at the same time. In this work, we propose a phase-only hologram compression and decompression scheme incorporating both JPEG standard and deep learning post-processing.