Low-Rank Sparse Tensor Approximations for Large High-Resolution Videos

Tensor decomposition techniques are becoming increasingly important in processing videos with large sizes and dimensions. Under the framework of CANDECOMP/PARAFAC decomposition (CPD), this work studies low-rank sparse tensor approximations (LRSTAs) to higher-order tensors. Both theoretical and practical properties are evaluated for LRSTAs to represent large high-resolution videos. The evaluation brings three major contributions of this work. Firstly, the theoretical connection between CPD for high-order tensors and traditional singular value decomposition (SVD) for matrices are established, and the tensor rank for traditional SVD is defined. This provides a theoretical basis to compare tensor-based approach against matrix-based approach under the framework of tensor decompositions. Secondly, the non-orthogonality of CPD and its implications are revealed. The solution set of an LRSTA can only be used as a whole. Thirdly, a computationally efficient algorithm is developed. Its practical properties are also investigated in object detection and recognition in high-resolution videos. The results of the experiments showed that the proposed algorithm can handle large high-resolution videos very efficiently in terms of memory allocation. Results also revealed that commonly used total variations may not be a good evaluation metric for real world applications in computer vision. LRSTAs should be evaluated using the end goal of the applications, such as the accuracy of object detection and recognition.