This paper proposes an efficient light field image coding (LFC) solution based on High Efficiency Video Coding (HEVC). The proposed light field codec makes use of the self-similarity (SS) compensated prediction concept to efficiently explore the inherent correlation of this type of content. To further improve the coding performance, a bi-predicted SS estimation and SS compensation is proposed, where the candidate predictor can be also devised as a linear combination of two blocks within the same search window. In addition, an improved vector prediction scheme is also used to take advantage of the particular characteristics of the SS prediction vectors. Experimental results show that the proposed LFC scheme is able to outperform the benchmark solutions with significant gains.