Low-rank tensor sensing is a fundamental problem with broad applications in signal processing and machine learning. Among various tensor models, low-Tucker-rank tensors are particularly attractive for capturing multi-mode subspace structures in high-dimensional data. Existing recovery methods either operate on the full tensor variable with expensive tensor projections, or adopt factorized formulations that still rely on full-gradient computations, while most stochastic factorized approaches are restricted to tensor decomposition settings. In this work, we propose a stochastic alternating minimization algorithm that operates directly on the core tensor and factor matrices under a Tucker factorization. The proposed method avoids repeated tensor projections and enables efficient mini-batch updates on low-dimensional tensor factors. Numerical experiments on synthetic tensor sensing demonstrate that the proposed algorithm exhibits favorable convergence behavior in wall-clock time compared with representative stochastic tensor recovery baselines.

翻译：低秩张量感知是信号处理与机器学习领域中具有广泛应用的基础性问题。在各种张量模型中，低Tucker秩张量因其能有效捕捉高维数据中的多模态子空间结构而备受关注。现有恢复方法要么在完整张量变量上进行计算并依赖昂贵的张量投影操作，要么采用仍需全梯度计算的因子化形式，而大多数随机因子化方法仅限于张量分解场景。本研究提出一种随机交替最小化算法，直接在Tucker分解框架下对核心张量与因子矩阵进行优化。该方法避免了重复的张量投影操作，并支持对低维张量因子进行高效的小批量更新。在合成张量感知任务上的数值实验表明，相较于代表性的随机张量恢复基线方法，所提算法在挂钟时间上展现出更优的收敛特性。