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Image-based rendering data sets, such as light fields, require efficient compression due to their large data size, but also easy random access when rendering from or streaming the data set. Efficient compression usually depends upon prediction between images, which creates dependencies between them, making random access more difficult. Independent encoding of the images is less efficient but provides random access, and in many cases is superior to predictive coding when considering the rate-distortion performance for certain viewing trajectories of the light field. In this paper, we describe a method which can obtain the best of both worlds: random access to any image; and compression efficiency, through predictive coding. We store multiple representations of each light field image, and decode using the appropriate representation depending on the available images that are already decoded. To eliminate prediction mismatch between the representations, we employ the idea of "SP-frames" from video coding. This allows us to generate identical reconstruction images from all representations. Our experimental results show a significant improvement in terms of view-trajectory-dependent rate-distortion performance over independent coding of the images.