Light fields are one of the emerging 3D representation formats with an effective potential to offer very realistic and immersive visual experiences. This capability comes at the cost of a very large amount of acquired data which practical use requires efficient coding solutions. This need was already addressed by the JPEG Pleno Light Field Coding standard for static light fields, which has specified two coding modes, named 4D-Transform and 4D-Prediction. While the first offers better compression performance for smaller baseline light fields, the second excels for larger baseline light fields. This paper intends to propose a novel light field coding mode, the Slanted 4D-Transform coding mode, which extends the 4D-Transform coding mode based on the conventional 4D-DCT, to offer better compression performance than both the available JPEG Pleno coding modes, independently of the baseline. The key idea is to apply first to each 4D block in the light field an adaptive, hierarchical geometric transformation, which makes the data in the block more energy-compaction friendly for the following 4D-DCT. The rate-distortion performance results show that the proposed Slanted 4D-Transform codec is able to outperform both the already standardized JPEG Pleno coding modes, showing BD-Rates gains of 31.03% and 28.30% for the 4D-Transform and 4D-Prediction modes, respectively, thus implying that a single coding mode can efficiently code all types of light fields.INDEX TERMS JPEG Pleno standard, Light field coding, 4D transform mode, 4D-DCT, Slant transform.