Condition of Regularization Solution Superior to LS Solution Based on MSE Principle

The condition of regularization solution superior to LS solution is deduced on the basis of the MSE principle.A statistic for testing this condition is constructed.If the null hypothesis is accepted with a significance level, it indicates that regularization solution is superior to LS solution, which also verifies that the determined regularization matrix and regularization factor are reasonable.On the contrary, if the null hypothesis is rejected, it means that the regularization method is unreasonably used.Since the regularization matrix and regularization factor is variant and can be changed,we can modify their values until the null hypothesis is accepted.The condition and its statistic given in this paper are fit for all kinds of Tikhonov regularization methods.