Subset selection for multi-Gabor and non-orthogonal wavelets expansions

Non-orthogonal wavelets and Gabor or Multi-windows Gabor expansions[1, 2, 3, 4] involving well-localized synthesis/analysis functions are characterized by being redundant. This entails that the signal modeling is carried out through a rank deficient linear transformation and the expansion coefficients are no unique. In the finite dimensional case one solution for the coefficients (which provides the coefficients of Minimum Norm) is approached by the pseudo-inverse of the concomitant rank deficient transformation. In many applications this makes a great deal of sense. In other applications, however, the model-builder is not interested in a predictor that involves all the redundant factors. Instead, a predictor constructed out of the independent factors is sought. How to pick these factors is a problem of subset selection [5] and we shall advance here a new method for accomplishing such a goal.