A collocation-type method for the solution of inverse problems in dispersive scattering theory

1995 ◽  
Vol 9 (1) ◽  
pp. 14-17 ◽  
Author(s):  
Mohsen Razzaghi ◽  
Falih Ahmad
Keyword(s):  
Inverse Problems ◽  
Scattering Theory ◽  
Type Method

The geometry of convex surfaces and inverse problems of scattering theory

1994 ◽  
Vol 35 (5) ◽  
pp. 845-862
Author(s):  
Yu. E. Anikonov ◽  
V. N. Stepanov
Keyword(s):  
Inverse Problems ◽  
Scattering Theory ◽  
Convex Surfaces

scholarly journals On a Level-Set Method for Ill-Posed Problems with Piecewise Nonconstant Coefficients

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
A. De Cezaro
Keyword(s):  
Inverse Problems ◽  
Level Set Method ◽  
Level Set ◽  
Regularization Method ◽  
Level Sets ◽  
Approximate Solutions ◽  
Type Method ◽  
Ill Posed ◽  
Level Set Approach ◽  
Level Set Framework

We investigate a level-set-type method for solving ill-posed problems, with the assumption that the solutions are piecewise, but not necessarily constant functions with unknown level sets and unknown level values. In order to get stable approximate solutions of the inverse problem, we propose a Tikhonov-type regularization approach coupled with a level-set framework. We prove the existence of generalized minimizers for the Tikhonov functional. Moreover, we prove convergence and stability for regularized solutions with respect to the noise level, characterizing the level-set approach as a regularization method for inverse problems. We also show the applicability of the proposed level-set method in some interesting inverse problems arising in elliptic PDE models.

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