Tensor Decomposition for High-Resolution Images and Videos

Tensor decompositions, including CANDECOMP/PARAFAC decomposition (CPD), Tucker decomposition (TKD), and tensor train decompositions (TTD), are extensions of singular value decomposition (SVD) for matrices. They are frameworks to decompose images or videos data into bases and coefficients. Due to recent developments in artificial intelligence (AI), tensor decomposition techniques are becoming increasingly important due to its compact representation, fast access , and easy reconstruction. However, tensor decompositions are still challenging in both computations and interpretations because CPD lacks orthogonality, TKD lacks sparsity, and TTD lacks both orthogonality and sparsity. To understand these issues, we evaluate their theoretical and practical limitations induced by the lack of orthogonality and sparsity in existing tensor decomposition methods. To overcome these limitations, a tensor decomposition method with both orthogo-nality and sparsity is proposed. Due to the two properties, the proposed method can be implemented by either a full decomposition or a partial decomposition version. Rather than the full decomposition version which always decomposes a given tensor into the sum of many rank-one tensors, the partial decomposition version only decomposes it into the sum of a number of outer products of lower-order tensors. This leads to the notation of eigen images, which reflects common important properties of images or videos with shared features. Eigen images are independent, meaning that they can be used to interpret the contents of images and videos. Experiment results show that the proposed method has small memory footprint and is much more efficient than existing tensor decomposition methods. Great advantages are demonstrated in conjunction with deep learning for object detection and recognition in high-resolution videos.