A Unified Framework for Compression and Compressed Sensing of Light Fields and Light Field Videos

In this article we present a novel dictionary learning framework designed for compression and sampling of light fields and light field videos. Unlike previous methods, where a single dictionary with one-dimensional atoms is learned, we propose to train a Multidimensional Dictionary Ensemble (MDE). It is shown that learning an ensemble in the native dimensionality of the data promotes sparsity, hence increasing the compression ratio and sampling efficiency. To make maximum use of correlations within the light field data sets, we also introduce a novel nonlocal pre-clustering approach that constructs an Aggregate MDE (AMDE). The pre-clustering not only improves the image quality but also reduces the training time by an order of magnitude in most cases. The decoding algorithm supports efficient local reconstruction of the compressed data, which enables efficient real-time playback of high-resolution light field videos. Moreover, we discuss the application of AMDE for compressed sensing. A theoretical analysis is presented that indicates the required conditions for exact recovery of point-sampled light fields that are sparse under AMDE. The analysis provides guidelines for designing efficient compressive light field cameras. We use various synthetic and natural light field and light field video data sets to demonstrate the utility of our approach in comparison with the state-of-the-art learning-based dictionaries, as well as established analytical dictionaries.