Remarks on choosing a regularization parameter using the quasioptimality and ratio criterion
USSR Computational Mathematics and Mathematical Physics
Original Article: Comparingparameter choice methods for regularization of ill-posed problems
Mathematics and Computers in Simulation
Original Article: Comparingparameter choice methods for regularization of ill-posed problems
Mathematics and Computers in Simulation
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Regularization is typically based on the choice of some parametric family of nearby solutions, and the choice of this family is a task in itself. Then, a suitable parameter must be chosen in order to find an approximation of good quality. We focus on the second task. There exist deterministic and stochastic models for describing noise and solutions in inverse problems. We will establish a unified framework for treating different settings for the analysis of inverse problems, which allows us to prove the convergence and optimality of parameter choice schemes based on minimization in a generic way. We show that the well known quasi-optimality criterion falls in this class. Furthermore we present a new parameter choice method and prove its convergence by using this newly established tool.