The Study Of Sparsity Constraint Regularization Method For Nonlinear Inversion Problems

In this paper, investigate the nonlinear inverse problem of sparsity constraint regularization. Because the problem is ill-posed, namely the numerical results of data are more sensitive, and observation data exist to noise, so must through the regularization method for the approximate solutions of the inverse problem, This method is used to solve the sparse solution is effective. The Tikhonov regularization of punishment is secondary, and its function is weaken the original ill-posed problem of the oscillation of the approximate solution, which has some of the approximate solution smoothness, and thereby giving the approximate solution of the stable. In the practical mathematical physics of the inverse problem of applications, there are solutions for discontinuous functions or contain cusp of function, this time the classic regularization method for the solution of the smooth and with the actual have deviation, and sparse regularization method (also called lp constraint regularization method) is can well the performance parameters of the larger part of the narrative.First, this paper through the application of the Landweber iteration method respectively introduces method:projected shrinkage interative algorithm and dual interative algorithm. With the two algorithms are solving the minimizer of the sparsity constraint functional, and giving the two algorithm’s convergence and stability estimate.Last, the exploration of seismic wave equation based on the 2-D wave velocity inversion problems. By using two kinds of different speed model validation method is effective. The theory analysis showed that:sparse constraint regularization method for discontinuous medium model has good recognition ability. Compared to the classic Landweber iterative method, projected shrinkage interative algorithm and dual interative algorithm can achieve good inversion results, not only effectively overcome the nonlinear inverse problem of discomfort qualitative, but also greatly reduce the computation time.