Over the years, the pursuit of capturing the precise visual information of a scenehas resulted in various enhancements in digital camera technology, such as highdynamic range, extended depth of field, and high resolution. However, traditionaldigital cameras only capture the spatial information of the scene and cannot pro-vide an immersive presentation of it. Light field (LF) capturing is a new-generationimaging technology that records the spatial and angular information of the scene. Inrecent years, LF imaging has become increasingly popular among the industry andresearch community mainly for two reasons: (1) the advancements made in optical and computational technology have facilitated the process of capturing and processing LF information and (2) LF data have the potential to offer various post-processing applications, such as refocusing at different depth planes, synthetic aperture, 3Dscene reconstruction, and novel view generation. Generally, LF-capturing devicesacquire large amounts of data, which poses a challenge for storage and transmissionresources. Off-the-shelf image and video compression schemes, built on assump-tions drawn from natural images and video, tend to exploit spatial and temporalcorrelations. However, 4D LF data inherit different properties, and hence there is aneed to advance the current compression methods to efficiently address the correla-tion present in LF data.

In this thesis, compression of LF data captured using a plenoptic camera andmulti-camera system (MCS) is considered. Perspective views of a scene capturedfrom different positions are interpreted as a frame of multiple pseudo-video se-quences and given as an input to a multi-view extension of high-efficiency videocoding (MV-HEVC). A 2D prediction and hierarchical coding scheme is proposedin MV-HEVC to improve the compression efficiency of LF data. To further increasethe compression efficiency of views captured using an MCS, an LF reconstructionscheme based on shearlet transform is introduced in LF compression. A sparse set of views is coded using MV-HEVC and later used to predict the remaining views by applying shearlet transform. The prediction error is also coded to further increase the compression efficiency. Publicly available LF datasets are used to benchmark the proposed compression schemes. The anchor scheme specified in the JPEG Plenocommon test conditions is used to evaluate the performance of the proposed scheme. Objective evaluations show that the proposed scheme outperforms state-of-the-art schemes in the compression of LF data captured using a plenoptic camera and an MCS. Moreover, the introduction of shearlet transform in LF compression further improves the compression efficiency at low bitrates, at which the human vision sys-tem is sensitive to the perceived quality.The work presented in this thesis has been published in four peer-reviewed con-ference proceedings and two scientific journals. The proposed compression solu-tions outlined in this thesis significantly improve the rate-distortion efficiency forLF content, which reduces the transmission and storage resources. The MV-HEVC-based LF coding scheme is made publicly available, which can help researchers totest novel compression tools and it can serve as an anchor scheme for future researchstudies. The shearlet-transform-based LF compression scheme presents a compre-hensive framework for testing LF reconstruction methods in the context of LF com-pression.