A Parameter Choice Strategy for the Inversion of Multiple Observations
It provides a theoretically grounded parameter selection strategy for geoscientific inverse problems with multiple observations, though the method is fairly general.
The paper proposes a general method for choosing parameters in multi-parameter models that combine multiple noisy observations, achieving accuracy within a constant factor of the noise level and the best approximation error.
In many geoscientific applications, multiple noisy observations of different origin need to be combined to improve the reconstruction of a common underlying quantity. This naturally leads to multi-parameter models for which adequate strategies are required to choose a set of 'good' parameters. In this study, we present a fairly general method for choosing such a set of parameters, provided that discrete direct, but maybe noisy, measurements of the underlying quantity are included in the observation data, and the inner product of the reconstruction space can be accurately estimated by the inner product of the discretization space. Then the proposed parameter choice method gives an accuracy that only by an absolute constant multiplier differs from the noise level and the accuracy of the best approximant in the reconstruction and in the discretization spaces.