Image subband coding using an information theoretic subband splitting criterion

It has been proved recently that for Gaussian sources with memory an ideal subband split will produce a coding gain for scalar or vector quantization of the subbands. Following the methodology of the proofs, we outline a method for successively splitting the subbands of a source, one at a time to obtain the largest coding gain. The subband with the largest theoretical rate reduction (TRR) is determined and split at each step of the decomposition process. The TRR is the difference between the rate in optimal encoding of N-tuples from a Gaussian source (or subband) and the rate for the same encoding of its subband decomposition. The TRR is a monotone increasing function of a so-called spectral flatness ratio, which involves the products of the eigenvalues of the source (subband) and subband decomposition covariance matrices of order N. These eigenvalues are estimated by the variances of the Discrete Cosine Transform, which approximates those of the optimal Karhunen Loeve Transform. After the subband decomposition hierarchy or tree is determined through the criterion of maximal TRR, each subband is encoded with a variable rate entropy constrained vector quantizer. Optimal rate allocation to subbands is done with the BFOS algorithm which does not require any source modelling. We demonstrate the benefit of using the criterion by comparing coding results on a two-level low-pass pyramidal decomposition with coding results on a two-level decomposition obtained using the criterion. For 60 MCFD (Motion Compensated Frame Difference) frames of the Salesman sequence an average rate-distortion advantage of 0.73 dB and 0.02 bpp and for 30 FD (Frame Difference) frames of Caltrain image sequence an average rate-distortion advantage of 0.41 dB and 0.013 bpp are obtained with the optimal decomposition over low-pass pyramidal decomposition.