Research on Numerically Solving the Inverse Problem Based on L1 Norm

Abstract

Abstract In this paper, the numerical solution method based on L1 norm for inverse problem is studied. First, according to the theory of the L1 norm and the characteristics of the problem to be solved, a cost function is constructed. Further, for complex parameter estimation problems and derivative discontinuities, the regularization method is used to construct the cost function and the Huber function is used in the derivative discontinuity. Finally, the problem is solved numerically by the semi-smooth Newton method. The experimental results show that the method based on L1 norm is an effective method under the interference of non-Gaussian noises. For the parameter estimation of complex models, the results based on the L1 norm method are very closer to the real parameters when there is impulse noise. For parameter estimation under non-Gaussian noise, the L1 norm estimation method has significant advantages over the L2 norm method.