Matched Filtering with Orthogonal Constraints

In this paper we outline a new method to improve the solution of the filter set estimation problem applied to the separation of two interfering wave-fields. The problem is well described in [Guitton, 2005] where the two data components are assumed to be non-Gaussian and the cost function is minimized by using a Hybrid L1/L2 norm. Another kind of hybrid-norm solver has been derived in [Costagliola et al, 2011]. Here we want to extend the latter by introducing an uncorrelation assumption. Our aim is to use this tool to better separate the full-wavefield starting from a preliminary estimation of its components. The problem can be casted as the minimization over the set of Stiefel matrices and it can be solved by SVD decomposition (plus additional iterations in a gradient based algorithm if the set is orthogonal but not necessary orthonormal). However, this procedure is not only non-linear and non-convex, but also numerically expensive. Thus, we reformulate the problem as a constrained optimization solved by a gradient based method that searches for the solution in the neighborhood of the unconstrained optimization solution. Results on synthetic and field data show that introducing orthogonality constraints can improve the wavefield component separation.