Rate-distortion analysis of backward adaptive transform coding schemes

The main advantage of backward over forward adaptive coding schemes is to update the coding parameters with the data available at the decoder, avoiding thereby any excess bit rate. The performances of two practical backward adaptive transform coding schemes are analyzed in terms of rate and distortion for two transforms: the KLT (Karhunen-Loeve transform) and the LDU transform (based on a lower-diagonal-upper factorization of the covariance matrix, R, of the data). For both algorithms, we model the expected distortion w.r.t. the number of vectors available at the decoder. Our analysis shows that, for an algorithm using Sheppard´s correction on the second order moment estimates, the distortion should converge to the target distortion. Without this correction, the effects of backward adaptation are shown to move the actual r(D) point of the system from the target point by the same term for both transforms. Simulation results confirming the theoretic analysis are presented.