In this paper, a new time-domain method is presented that yields sparse radon panels. This method estimates a sparse model by adding two models estimated independently with only positive or negative values obtained with a bound-constrained optimization technique. Therefore, by forcing the model to fall within a certain range of values, the null space and its effects are decreased.
In the section following this introduction, I introduce the problem of finding a bound-constrained model and its resolution by presenting the limited memory L-BFGS-B technique Zhu et al. (1997). This method aims at finding a solution with simple bounds for linear or non-linear problems. Then, I introduce a method that estimates sparse radon domains. Finally, this technique is tested on a synthetic and field data examples and compared to the Cauchy regularization Sacchi and Ulrych (1995). They demonstrate that the proposed strategy yields sparse radon panels comparable to the Cauchy approach. One advantage of this new strategy is that the choice of parameters is much simpler; for instance, no Lagrange multiplier is needed. One drawback is that two inversions need to be carried out as opposed to one for the Cauchy method.