Energy Constraint Scarce Wavelet

In this paper we introduce a generalization of the best basis wavelet packet method which selects a suboptimal best basis out of a restricted library of wavelet packet bases. For a given image this restricted library is generated by a 2D separable multiresolution analysis which discriminates branches of the resulting quadtree structured representation of the image according to a measure of energy-compaction. Thus we get a family of scarce libraries (w.r.t. the full wavelet packet library) parameterized by a so-called energy-threshold. This energythreshold parameter allows a truncation of energetically irrelevant branches and hence a control of the complexity of the best-basis algorithm ranging from the low complexity standard DWT to the high complexity full best-basis algorithm. Our experimental results for image coding applications show that the rate-distortion (RD) performance increases in distinguished (image dependent) jumps as the energy-threshold decreases. As a consequence, the instrument of energy-thresholding can be used to nd optima with relatively high RD performance and relatively low complexity.