  In this manuscript, a purely data driven statistical regularization method is
proposed for extracting the information from big data with randomly distributed
noise. Since the variance of the noise maybe large, the method can be regarded
as a general data preprocessing method in ill-posed problems, which is able to
overcome the difficulty that the traditional regularization method unable to
solve, and has superior advantage in computing efficiency. The unique
solvability of the method is proved and a number of conditions are given to
characterize the solution. The regularization parameter strategy is discussed
and the rigorous upper bound estimation of confidence interval of the error in
$L^2$ norm is established. Some numerical examples are provided to illustrate
the appropriateness and effectiveness of the method.
