An iterated multiplicative regularization for force reconstruction problems

In presence of very noisy data, standard regularization methods generally fail in reconstructing satisfying solutions. To this end, iterated regularization techniques can be implemented. This class of regularization approaches can be seen as an iterative refinement of an initial solution obtained from classical regularization methods. In the present paper, an iterated multiplicative regularization for dealing with force reconstruction problems is discussed. More specifically, the associated non-stationary formulation is compared to its stationary counterpart through numerical and experimental validations. It is shown that the proposed stationary version outperforms the non-stationary formulation regarding the quality of reconstructed solutions.