On a space-time regularization for force reconstruction problems

Tikhonov and LASSO regularizations are commonly used to solve force reconstruction problems in time domain. Unfortunately, these particular forms of additive regularization are not well adapted to tackle both localization and time reconstruction problems simultaneously, since they are generally restricted to the reconstruction of sources sharing the same space and time characteristics. To alleviate this limitation, a multiplicative space-time regularization is introduced. The proposed regularization strategy takes advantage of one's prior knowledge of the space-time characteristics of excitation sources. It also introduces a novel reconstruction model based on the generalized-α method, which is unconditionally stable and second-order accurate. The validity of the proposed method is assessed numerically and experimentally. In particular, comparisons with standard regularization terms point out the practical benefit in exploiting both spatial and temporal prior information simultaneously in terms of quality and robustness of reconstructed solutions.