Randomized regularized Kaczmarz algorithms have recently been proposed to solve tensor recovery models with {\it consistent} linear measurements. In this work, we propose a novel algorithm based on the randomized extended Kaczmarz algorithm (which converges linearly in expectation to the unique minimum norm least squares solution of a linear system) for tensor recovery models with {\it inconsistent} linear measurements. We prove the linear convergence in expectation of our algorithm. Numerical experiments on a tensor least squares problem and a sparse tensor recovery problem are given to illustrate the theoretical results.

翻译：最近有人提议采用随机化的卡茨马尔兹常规算法,用 ~它一致的线性测量法解决抗拉恢复模型。在这项工作中,我们提议采用一种新的算法,以随机化的扩展卡茨马尔兹算法为基础(该算法以线性系统独有的最低限度标准最低方形解决方案为依线性趋同),用线性测量法解决抗拉恢复模型。我们证明了我们算法的线性趋同。用数字性实验用一个最差方形的问题和稀有的抗拉恢复问题来说明理论结果。