Optimal vector pyramidal and subband decompositions for the coding of multichannel signals

Filters are determined which achieve optimal construction of multiresolution vector sequences by minimizing the variance of the error signals between successive pyramid levels. A measure of the entropy reduction achieved by the pyramid is in this way maximized. Further, the filters are also determined which minimize the error committed when only the low resolution vector signal is retained from a multi-channel perfect reconstruction vector filter bank. The effect of this is to ensure that the lower-resolution image produced by the primary subband bears maximum resemblance to the input image. In both settings, it is assumed that additive transmission noise corrupts the downsampled signal prior to the synthesis stage. It is seen that under noiseless or lossless transmission conditions, the two above families of optimal analysis and synthesis filters coincide. The results are evaluated experimentally for the vector coding of the DCT coefficients.