  In this paper, we apply randomized algorithms to approximate the total least
squares (TLS) solution of the problem $Ax\approx b$ in the large-scale discrete
ill-posed problems. A regularization technique, based on the multiplicative
randomization and the subspace iteration, is proposed to obtain the approximate
core problem.In the error analysis, we provide upper bounds %in terms of the
$(k\!\!+\!\!1)$-th singular value of $A$ for the errors of the solution and the
residual of the randomized core reduction. Illustrative numerical examples and
comparisons are presented.
