  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.
