A tree code, asymptotically optimal for stationary Gaussian sources and squared error distortion, is applied suboptimally to encode the discrete cosine transform (DCT) of image subblocks. The variance spectrum of each block DCT is estimated and specified uniquely by a set of one-dimensional autoregressive parameters. The average pel rate for each block is allowed to vary to meet the specification of the same average distortion per block. Since the variance spectrum and rate are different for every block. so is the code tree. Comparative coding simulations with a 256*256 and 512*512 image show that DCT tree coding with postcoding is clearly superior to DCT quantization and that a variable block rate assignment gains about 3 dB over a fixed block rate assignment.>

A transform tree code, theoretically optimal for stationary Gaussian sources and the squared-error distortion measure at all rates, is adaptively applied in a blockwise fashion to the encoding of images. The rate of the basic tree code is 0.5 bits/pel and the overhead rate ranges from .24 to .36 bits/pel. A smoothing and block quantization is used for effective reduction of the rate for transmitting a set of eigenvalue estimates, which comprise the main contribution to the overhead. In encoding simulations the adaptation with smoothing and quantization gave better performance with a block size of 16 at lower search intensity and with more uniformity and less blocking effect. At a block size of 32, where the reconstruction quality is higher, the same adaptation technique yielded nearly the same results as the non-adaptive one at the same overall rate, but with a savings of search and computational complexity.

A new tree code is introduced for discrete-time stationary Gaussian sources with hounded, integrable power spectra and the squared-error distortion measure. The codewords in the tree are reconstructions of Karhunen-Loève transforms of the source words. The branching factor and the number of code letters per branch may vary with level in the tree. A theorem that guarantees the existence of an optimal code for any code rate using such a tree is proved. The proof uses the random coding argument in conjunction with a theorem on survival of a branching process with random environment. A suboptimal but computationally affordable realization of the theorem's coding technique was used for encoding simulations for six autoregressive sources at rates of1.0, 0.50, 0.25, and0.10bits per source symbol. The average distortion results were generally within1dB of the distortion-rate bound but varied widely depending on the source and rate. The results were compared with those for transform quantization simulations for the same sources and rates. The tree code always performed better but only by an average of0.44dB all sources and rates. Longer source blocks and more intensive search would certainly improve the performance of the tree codes, but at the expense of extra computation and storage.

We have utilized for image coding a transform tree coding technique that is theoretically optimal for Gaussian sources and the squared error criterion at all nonzero rates. In the interest of affordable computation, we used a suboptimal discrete cosine transform to encode image sub-blocks and a selective search through the code tree. Coding simulations of a woman's face image at rates of 1.0 and 0.25 bits/pel gave good to excellent results. The rate 1.0 results were superior to previous ones using another tree coding method. Until now there have been no reported results with searched codes for images using a rate under 1.0 bit/pel. Encoding a computer-generated image source indicated SNR performance about 2dB less than the optimal SNR of the rate-distortion bound.

We seek to evaluate the efficiency of hybrid transform/ DPCM interframe image coding relative to an optimal scheme that minimizes the mean-squared error in encoding a stationary Gaussian image sequence. The stationary assumption leads us to use the asymptotically optimal discrete Fourier transform (DFT) on the full frame of an image. We encode an actual image sequence with full-frame DFT/DPCM at several rates and compare it to previous interframe coding results with the same sequence. We also encode a single frame at these same rates using a full-frame DFT to demonstrate the inherent coding gains of interframe transform DPCM over intraframe coding. We then generate a pseudorandom image sequence with precise Gauss-Markov statistics and encode it by hybrid full-frame DFT/DPCM at various rates. We compare the signal-to-noise ratios (SNR's) of these reconstructions to the optimal ones calculated from the rate-distortion function. We conclude that in a medium rate range below 1 bit/pel/frame where reconstructions for hybrid transform/ DPCM may be unsatisfactory, there is enough margin for improvement to consider more sophisticated coding schemes.

A non-adaptive scheme for encoding an image sequence is described that yields better results than any previous comparable interframe image coding method. The scheme uses a hybrid of two-dimensional transform coding for the spatial dimension and DPCM for the time dimension similar to some previous works [e.g., 1]. Unlike the previous efforts, which use discrete cosine transforms (DCT's) of image subblocks and suboptimal quantization, we utilize a full image DFT and an optimal quantization algorithm. The results with the standard sixteen frame sequence of Walter Cronkite are visually superior to previous transform coding efforts, especially at rates lower than 1 bit/pixel/ frame. The signal-to-noise ratios are higher than those of nonadaptive hybrid DCT/DPCM in [1] by 2.6 to 10.5 dB depending on rate.