标题： 对数求和正则化高阶张量恢复的Kaczmarz算法 显示英文标题

标题： Log-Sum Regularized Kaczmarz Algorithms for High-Order Tensor Recovery

摘要： 稀疏和低秩张量恢复已成为一个重要的研究领域，其应用涉及计算机视觉等多个领域。 然而，最小化向量的$\ell_0$-范数或矩阵的秩是NP难的。 因此，由于计算效率的原因，通常在实际中采用它们的凸松弛版本，例如对数和惩罚。 在本工作中，我们提出了用于恢复具有稀疏或低秩结构的高阶张量的新颖对数和正则化Kaczmarz算法。 我们提出了块变体并给出了所提出算法的收敛性分析。 在合成和真实世界数据集上的数值实验表明了所提出方法的有效性。 显示英文摘要

摘要： Sparse and low rank tensor recovery has emerged as a significant area of research with applications in many fields such as computer vision. However, minimizing the $\ell_0$-norm of a vector or the rank of a matrix is NP-hard. Instead, their convex relaxed versions are typically adopted in practice due to the computational efficiency, e.g., log-sum penalty. In this work, we propose novel log-sum regularized Kaczmarz algorithms for recovering high-order tensors with either sparse or low-rank structures. We present block variants along with convergence analysis of the proposed algorithms. Numerical experiments on synthetic and real-world data sets demonstrate the effectiveness of the proposed methods.