This paper proposes fast randomized algorithms for computing the Kronecker Tensor Decomposition (KTD). The proposed algorithms can decompose a given tensor into the KTD format much faster than the existing state-of-the-art algorithms. Our principal idea is to use the randomization framework to reduce computational complexity significantly. We provide extensive simulations to verify the effectiveness and performance of the proposed randomized algorithms with several orders of magnitude acceleration compared to the deterministic one. Our simulations use synthetics and real-world datasets with applications to tensor completion, video/image compression, image denoising, and image super-resolution

翻译：本文提出了用于计算Kronecker张量分解的快速随机化算法。所提出的算法能够以远快于现有最先进算法的速度将给定张量分解为KTD格式。我们的核心思想是利用随机化框架显著降低计算复杂度。通过大量仿真实验验证了所提随机化算法的有效性，相较于确定性算法实现了数个数量级的加速。我们的仿真实验采用合成数据集和真实数据集，涵盖了张量补全、视频/图像压缩、图像去噪和图像超分辨率等应用场景。