Prediction of coefficients from coarse to fine scales in the complex wavelet transform

Prediction of fine scale DWT coefficients from coarser scales is not generally possible. On the other hand, the redundancy of the shift-invariant complex wavelet transform (CWT) should allow good coarse-to-fine scale prediction. The CWT's magnitude and phase step responses are well-behaved functions of a coefficient's normal distance to an edge. We present a coefficient prediction algorithm which assumes an edge-based image model. The algorithm infers information about local edges from coarse scale coefficients, and predicts the effect of these edges on the magnitudes and phases of finer level coefficients. Accurate coarse-to-fine prediction of coefficients has important potential benefits for image coding and resolution enhancement systems.