论文信息 - State-Space Regularization: Geometric Theory

State-Space Regularization: Geometric Theory

Abstract. Regularization of nonlinear ill-posed inverse problems is analyzed for a class of problems that is characterized by mappings which are the composition of a well-posed nonlinear and an ill-posed linear mapping. Regularization is carried out in the range of the nonlinear mapping. In applications this corresponds to the state-space variable of a partial differential equation or to preconditioning of data. The geometric theory of projection onto quasi-convex sets is used to analyze the stabilizing properties of this regularization technique and to describe its asymptotic behavior as the regularization parameter tends to zero.

Karl Kunisch | G. Chavent | K. Kunisch | G. Chavent

[1] C. Kravaris,et al. Identification of parameters in distributed parameter systems by regularization , 1983, The 22nd IEEE Conference on Decision and Control.

[2] Guy Chavent. Quasi-convex sets and size × curvature condition, application to nonlinear inversion , 1991 .

[3] C. W. Groetsch,et al. The theory of Tikhonov regularization for Fredholm equations of the first kind , 1984 .

[4] K. Kunisch,et al. A geometric theory forL2-stability of the inverse problem in a one-dimensional elliptic equation from anH1-observation , 1993 .

[5] Karl Kunisch,et al. Regularization in state space , 1993 .

[6] K. Kunisch,et al. Convergence of Tikhonov regularization for constrained ill-posed inverse problems , 1994 .

[7] Guy Chavent. New size×curvature conditions for strict quasiconvexity of sets , 1991 .