Parameter Identification Problem Of Sparse Constrained Regularization Method And Application

Parameter identification is an important kind of the inverse problems, which has drawn much attention of the researchers. However, with the rapid development of the technology in recent years, people are no longer satisfied with the simple parameter identification problems. More attention is paid to how could we rapidly and accurately identify the changes of parameters, so as to extend the traditional static parameter inversion to the dynamic parameter inversion and identify the dynamic changes of parameters accurately. Compared with the traditional parameter identification problem, this kind of problem, such as the time-lapse seismic, has gained many attention in recent years.This paper mainly focuses on the algorithm and the application for the variation identification problem by using the sparse constraint regularization. We first introduce the current research on the parameter identification and the sparse constraints regularization. Then we give the background, purpose and significance of the research.After that, we introduce the related sparse constraint regularization theory, and analyze the sparse representation of the solution of the parameter identification problem. Numerical tests prove the feasibility of the sparse optimization method for solving such problem.Then, we analyze the characteristics of the parameter identification problem and introduce the localized inversion model which effectively describes the parameter identification problem. The objective functional based on a combination of the norm-2l and norm-1l is presented. After obtaining the objective functional, the mixed regularized inversion algorithm is developed. This inversion algorithm finds the solution by two steps, the regular Gauss-Newton method and the soft threshold shrinkage method. Finally, numerical simulations for three simplified models prove the effectiveness of the inversion algorithm. The applicability of the algorithm is also demonstrated by analyzing the error curve of different parameters.