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A Novel Approach for Adaptive Bayesian Prior Selection in Ill-conditioned Measurement Problems

A novel approach for ill-conditioned inverse problems' solution is presented. In the novel approach the prior knowledge about the quantity to be estimated, necessary to combat the ill-conditioning of the problem, is not a priori assigned; it is instead adaptively determined on the basis of the available measurement data. The suggested estimator is particularly suited in case the measurement process is performed in a very limited context of knowledge about the measurand, and, as a consequence, the selection of proper prior knowledge may become a difficult task.