Universal transform coding based on backward adaptation

The method for universal transform coding based on backward adaptation introduced by Goyal et al. (see IEEE Int. Conf. Image Proc., vol.II, p.365-8, 1996) is reviewed and further analyzed. This algorithm uses a linear transform which is periodically updated based on a local Karhunen-Loeve transform (KLT) estimate. The KLT estimate is derived purely from quantized data, so the decoder can track the encoder state without any side information. The effect of estimating only from quantized data is quantitatively analyzed. Two convergence results which hold in the absence of estimation noise are presented. The first applies for any vector dimension but does not preclude the necessity of a sequence of quantization step sizes that goes to zero. The second applies only in the two-dimensional case, but shows local convergence for a fixed, sufficiently small quantization step size. Refinements which reduce the storage and computational requirements of the algorithm are suggested.