Adaptive regularization parameter adjustment for reconstruction problems

In reconstruction (i.e., determining the states of a model from measurements of model outputs), one is often forced to search for a regularized solution due to poor sensitivity of model outputs with respect to the model states. The amount of regularization is controlled by the regularization parameter, a scalar value multiplied with the so-called regularization term. The choice of the regularization parameter is crucial for the reconstruction process. In this paper, a new method to estimate the regularization parameter in an adaptive way is proposed. A condition-number based estimate of the regularization parameter for the first iteration step is required to choose the weighting factor for adapting the regularization parameter iteratively. By virtue of controlling the regularization term, a kind of edge preservation can be achieved. The validity of this method will be demonstrated for a capacitance tomography problem, which is solved applying a Gauss-Newton scheme.