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In this paper, we present a novel compression technique for Bidirectional Texture Functions based on a sparse tensor decomposition. We apply the K-SVD algorithm along two different modes of a tensor to decompose it into a small dictionary and two sparse tensors. This representation is very compact, allowing for considerably better compression ratios at the same RMS error than possible with current compression techniques like PCA, N-mode SVD and Per Cluster Factorization. In contrast to other tensor decomposition based techniques, the use of a sparse representation achieves a rendering performance that is at high compression ratios similar to PCA based methods.