Tree coding of image sub-bands

It is proved that optimal coding of image subbands achieves the ultimate rate-distortion performance for Gaussian sources with squared-error distortion. Optimal performance is achieved only asymptotically with infinite-size source sequences. The approach of the rate-distortion function of finite-size sequences to its limit is investigated and a bound is derived that shows a potentially closer approach for coding subbands that for the full band. A suboptimal realization of an optimal tree coding method is used to encode both the full-band image and its subbands at 1.0 bit per pixel. The subband tree-coded image is more than 2 dB better in SNR and its overall performance is nearly comparable to that of the best schemes known to date