A STUDY ON STATISTICAL METHOD FOR REGULARIZATION NON – LINEAR INVERSE PROBLEMS

Author (s) : Mrs.V.Nandhini & Mr.S.K.Ganesh Babu, B.Priya

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Abstract :
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and allow a robust approximation of ill-posed (pseudo-) inverses. In the last two decades interest has shifted from linear to nonlinear regularization methods, even for linear inverse problems. The aim of this paper is to provide a reasonably comprehensive overview of this shift towards modern nonlinear regularization methods, including their analysis, applications and issues for future research. In particular we will discuss variational methods and techniques derived from them, since they have attracted much recent interest and link to other fields, such as image processing and compressed sensing. We further point to developments related to statistical inverse problems, multiscale decompositions and learning theory. Nonlinear inverse problems are much more difficult to solve than linear ones and the corresponding theory is far less developed. Each particular problem may demand a specific regularization. Nevertheless, one can formulate and analyze basic versions of nonlinear Tikhonov regularization and nonlinear iterative methods. These basic versions serve as starting points for regularizations adapted to our nonlinear model problems. Nonlinear Tikhonov regularization leads to nonlinear least squares problems.

Keywords : Tikhonov regularization, linear equation, Non - linear equation, Non - linear inverse equation.

Conference Date : 17/09/2021

Pages : 259

Paper ID : IESMDT257