2D wavelet transforms with a spatially adaptive 2D low pass filter
Charith Abhayaratne · 2004
Wavelet transforms that have an adaptive low pass filter are useful in applications where it requires the signal singularities, sharp transitions and image edges to be left intact in low pass subbands. In such applications it is vital to have low pass subbands that are not affected with smoothing artifacts associated with uniform low pass filtering. Previously, we presented a framework for designing 1D wavelets that have a spatially adaptive low pass filter using the prediction first lifting scheme, in which the adaptivity decisions are computed using wavelet (high pass) coefficients and no bookkeeping is required for the perfect reconstruction. In this paper, we extend the 1D scheme to design 2D wavelets that have a spatially adaptive low pass filter. We use 2D polyphase matrix of the corresponding 2D separable transform and compute the 2D lifting factorization steps. This scheme leads to non separable 2D adaptivity decisions, which is the preferred case for images, as opposed to the separable 2D realization using 1D transforms.