Complexity-scalable transform coding using variable complexity algorithms

In applications where compression has to be performed under varying complexity constraints (e.g., with hardware having to operate in reduced power mode) it is beneficial to design compression algorithms that allow some degree of complexity scalability. In this paper we explore complexity scalability for transform coding algorithms. We show that a variable complexity algorithm (VCA), which uses energy thresholds to determine the number of coefficients to be computed for each input, is preferable to other alternatives such as a pruned transform, where the same number of coefficients is computed for the whole image. We show that the benefits include not only a higher degree of scalability, but also increased compression performance, as we take advantage of the energy classification that is needed for VCA operation and design quantizers that match each class. We provide expressions for the average complexity as well as rate/distortion relations for a generic N-point VCA transform. For a two point case, we present closed-form relations describing the variance changes in two classes. In addition, rate-distortion-complexity relations are also empirically obtained. We apply VCA to eight-point KLT and 8×8 DCT in the JPEG framework and experiments show that the VCA approach is superior in rate/distortion performance at low rates compared to the standard transform coding techniques