  It is well known that Tikhonov regularization is one of the most commonly
used methods for solving ill-posed problems. One of the most widely applied
approaches is based on constructing a new dataset whose sample size is greater
than the original one. The enlarged sample size may bring additional
computational difficulties. In this paper, we aim to make full use of Tikhonov
regularization and develop a dual based semismooth Newton (DSSN) method without
destroying the structure of dataset. From the point of view of theory, we will
show that \blue{the DSSN method is a globally convergent method with at least
R-superlinear rate of convergence.} In the numerical computation aspect, we
evaluate the performance of the DSSN method by solving a class of sparse
Tikhonov regularization with high-dimensional datasets.
