In this manuscript, we introduce a tensor-based approach to Non-Negative Tensor Factorization (NTF). The method entails tensor dimension reduction through the utilization of the Einstein product. To maintain the regularity and sparsity of the data, certain constraints are imposed. Additionally, we present an optimization algorithm in the form of a tensor multiplicative updates method, which relies on the Einstein product. To guarantee a minimum number of iterations for the convergence of the proposed algorithm, we employ the Reduced Rank Extrapolation (RRE) and the Topological Extrapolation Transformation Algorithm (TEA). The efficacy of the proposed model is demonstrated through tests conducted on Hyperspectral Images (HI) for denoising, as well as for Hyperspectral Image Linear Unmixing. Numerical experiments are provided to substantiate the effectiveness of the proposed model for both synthetic and real data.

翻译：本文提出了一种基于张量的非负张量分解方法。该方法通过爱因斯坦积实现张量降维。为保持数据的正则性与稀疏性，我们施加了特定约束条件。此外，我们提出了一种基于爱因斯坦积的张量乘法更新优化算法。为确保算法收敛所需的最小迭代次数，我们采用了降秩外推法与拓扑外推变换算法。通过在去噪任务与高光谱图像线性解混任务中对高光谱图像进行测试，验证了所提模型的有效性。数值实验进一步证明了该模型在合成数据与真实数据上的优越性能。