This paper explores a new version of the Levenberg-Marquardt algorithm used for Tensor Canonical Polyadic (CP) decomposition with an emphasis on image compression and reconstruction. Tensor computation, especially CP decomposition, holds significant applications in data compression and analysis. In this study, we formulate CP as a nonlinear least squares optimization problem. Then, we present an iterative Levenberg-Marquardt (LM) based algorithm for computing the CP decomposition. Ultimately, we test the algorithm on various datasets, including randomly generated tensors and RGB images. The proposed method proves to be both efficient and effective, offering a reduced computational burden when compared to the traditional Levenberg-Marquardt technique.

翻译：本文探索了一种新型Levenberg-Marquardt算法，用于张量正则多路分解（CP分解），重点关注图像压缩与重建。张量计算，特别是CP分解，在数据压缩与分析中具有重要应用。本研究将CP分解形式化为非线性最小二乘优化问题，随后提出一种基于Levenberg-Marquardt的迭代算法用于求解CP分解。最终，我们在多种数据集（包括随机生成张量与RGB图像）上测试该算法。实验证明，与传统Levenberg-Marquardt方法相比，所提方法在降低计算负担的同时兼具高效性与有效性。