Highly Nonlinear Approximations for Sparse Signal Representation

Recursive updating/downdating of oblique projectors

Here we provide the equations for updating and downdating oblique projectors in order to account for the following situations:

Let us consider that the oblique projector onto the subspace along a given subspace is known. If the subspace is enlarged to by the inclusion of one element, i.e., , we wish to construct from the availability of . On the other hand, if the subspace is reduced by the elimination of one element, say the -th one, we wish to construct the corresponding oblique projector from the knowledge of . The subspace is assumed to be fixed. Its orthogonal complement in changes with the index to satisfy .