INTRODUCING THE LOCALLY STATIONARY DUAL-TREE COMPLEX WAVELET MODEL

This paper reconciles Kingsbury's dual-tree complex wavelets with Nason and Eckley's locally stationary model. We here establish that the dual-tree wavelets admit an invertible de biasing matrix and that this matrix can be used to invert the covariance relation. We also show that the added directional selectivity of the proposed model adds utility to the standard two-dimensional local stationary model. Non-stationarity detection on random fields is used as a motivating example. Experiments confirm that the dual-tree model can distinguish anisotropic non-stationarities significantly better than the current model.