Regularization networks for inverse problems: A state-space approach (Q1868083)

The solution of inverse problems through the regularization method yields a regularization network. Once the activation functions are known, the inverse problem can then be solved without any form of numerical integration. By exploiting the state-space representation and the Bayesian interpretation of regularization, it is shown how to compute the activation functions of the regularization network as well as the matrices needed to compute the weights, which can be computed in \(O(N)\) operations through Kalman filtering techniques. Finally, the algorithms are successfully applied to a real-world problem arising in the study of glandular hormone secretion.