Extract the information via multiple repeated observations under randomly distributed noise

Author:

Zhong Min1,Li Xinyan2,Liu Xiaoman2

Affiliation:

1. School of Mathematics , Southeast University , 210096: and Nanjing Center for Applied Mathematics, 211135 , Nanjing , Jiangsu Province , P. R. China

2. School of Mathematical Science , Fudan University , 200433 , Shanghai , P. R. China

Abstract

Abstract Extracting the useful information has been used almost everywhere in many fields of mathematics and applied mathematics. It is a classical ill-posed problem due to the unstable dependence of approximations on small perturbation of the data. The traditional regularization methods depend on the choice of the regularization parameter, which are closely related to an available accurate upper bound of noise level; thus it is not appropriate for the randomly distributed noise with big or unknown variance. In this paper, a purely data driven statistical regularization method is proposed, effectively extracting the information from randomly noisy observations. The rigorous upper bound estimation of confidence interval of the error in L 2 L^{2} norm is established, and some numerical examples are provided to illustrate the effectiveness and computational performance of the method.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

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