Light field imaging enables some post-processing capabilities like refocusing, changing view perspective, and depth estimation. As light field images are represented by multiple views they contain a huge amount of data that makes compression inevitable. Although there are some proposals to efficiently compress light field images, their main focus is on encoding efficiency. However, some important functionalities such as viewpoint and quality scalabilities, random access, and uniform quality distribution have not been addressed adequately. In this paper, an efficient light field image compression method based on a deep neural network is proposed, which classifies multiple views into various layers. In each layer, the target view is synthesized from the available views of previously encoded/decoded layers using a deep neural network. This synthesized view is then used as a virtual reference for the target view inter-coding. In this way, random access to an arbitrary view is provided. Moreover, uniform quality distribution among multiple views is addressed. In higher bitrates where random access to an arbitrary view is more crucial, the required bitrate to access the requested view is minimized.